Similarity relation is one of the spatial relations in the community of geographic information science and cartography.It is widely used in the retrieval of spatial databases, the recognition of spatial objects from i...Similarity relation is one of the spatial relations in the community of geographic information science and cartography.It is widely used in the retrieval of spatial databases, the recognition of spatial objects from images, and the description of spatial features on maps.However, little achievements have been made for it by far.In this paper, spatial similarity relation was put forward with the introduction of automated map generalization in the construction of multi-scale map databases;then the definition of spatial similarity relations was presented based on set theory, the concept of spatial similarity degree was given, and the characteristics of spatial similarity were discussed in detail, in-cluding reflexivity, symmetry, non-transitivity, self-similarity in multi-scale spaces, and scale-dependence.Finally a classification system for spatial similarity relations in multi-scale map spaces was addressed.This research may be useful to automated map generalization, spatial similarity retrieval and spatial reasoning.展开更多
Ocean observations are inherently characterized by irregular temporal and spatial distributions,as well as heterogeneous spatial resolutions and error characteristics arising from the use of diverse observational plat...Ocean observations are inherently characterized by irregular temporal and spatial distributions,as well as heterogeneous spatial resolutions and error characteristics arising from the use of diverse observational platforms and techniques.To enable their application across a broad range of scientific and practical problems,it is essential to map these heterogeneous datasets into temporally and spatially consistent gridded products.Optimal Interpolation remains the most widely adopted algorithm for the mapping of oceanographic data.Two principal implementations of the optimal interpolation algorithm are commonly employed.The first,known as the basic optimal interpolation,is derived from the theory of optimal estimation and involves computationally intensive matrix operations,posing significant challenges when applied to high-dimensional problems.The second,referred to as the point-wise optimal interpolation,reduces computational complexity through point-wise estimation,thereby circumventing high-dimensional operations;however,this approach results in a substantially higher overall computational cost.In this study,a novel optimal interpolation algorithm is proposed that utilizes the Kronecker product to approximate the background error covariance matrix.This formulation enables the decomposition of high-dimensional matrix operations into smaller,computationally tractable sub-problems,thereby improving the scalability of optimal interpolation for large spatial domains with dense observational coverage.Building upon this framework,a multi-scale optimal interpolation method is further developed to enhance the integration of observational datasets with widely varying spatial resolutions,thereby improving the accuracy and applicability of the resulting gridded products.展开更多
The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity d...The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.展开更多
In this paper, we discuss the relationship between k-semi-stratifiable spaces and quais-Nagata spaces and some mapping properties of quasi-Nagata spaces. We get following results: sequence-covering closed mapping pres...In this paper, we discuss the relationship between k-semi-stratifiable spaces and quais-Nagata spaces and some mapping properties of quasi-Nagata spaces. We get following results: sequence-covering closed mapping preserve quasi-Nagata spaces, and finite-to-one open mappings don't preserve quasi-Nagata spaces.展开更多
In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are inv...In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated.Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively.The results thus extend and improve some recent corresponding results.展开更多
In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These res...In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples.展开更多
In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman＇s th...In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman＇s theorem, Roth＇s theorem and Petryshyn＇s theorem are extended to condensing mappings satisfying the interior condition.展开更多
Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significan...Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes.In this study,we constructed a global urban structure(GUS-3D)dataset,including building volume,height,and footprint information,at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples.Our analysis indicated that the total volume of buildings worldwide in2015 exceeded 1×10^(12)m^(3).Over the 1985 to 2015 period,we observed a slight increase in the magnitude of 3D building volume growth(i.e.,it increased from 166.02 km3 during the 1985–2000 period to 175.08km3 during the 2000–2015 period),while the expansion magnitudes of the two-dimensional(2D)building footprint(22.51×10^(3) vs 13.29×10^(3)km^(2))and urban extent(157×10^(3) vs 133.8×10^(3)km^(2))notably decreased.This trend highlights the significant increase in intensive vertical utilization of urban land.Furthermore,we identified significant heterogeneity in building space provision and inequality across cities worldwide.This inequality is particularly pronounced in many populous Asian cities,which has been overlooked in previous studies on economic inequality.The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.展开更多
Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this cont...Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.展开更多
Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding r...Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.展开更多
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed poin...Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.展开更多
This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =αnu＋（1-αn）Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty...This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =αnu＋（1-αn）Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.展开更多
In this article,some coupled coincidence point results for two mappings g:X→X and G:X×X→X satisfying F-contractive type conditions are obtained,and some coupled fixed point results are derived in partially orde...In this article,some coupled coincidence point results for two mappings g:X→X and G:X×X→X satisfying F-contractive type conditions are obtained,and some coupled fixed point results are derived in partially ordered metric spaces.A sufficient condition for uniqueness of coupled point of coincidence are established for F type contraction,and a coupled common fixed point theorem is obtained.Some examples are given to support our results.展开更多
This paper is an attempt to investigate systematically fixed points of weakly inward maps by using some basic results from differential equations in Banach spaces. By investigating the Poincare operators for such diff...This paper is an attempt to investigate systematically fixed points of weakly inward maps by using some basic results from differential equations in Banach spaces. By investigating the Poincare operators for such differential equations, we establish a fixed point index theory for two classes of weakly inward maps.展开更多
Transportation systems are experiencing a significant transformation due to the integration of advanced technologies, including artificial intelligence and machine learning. In the context of intelligent transportatio...Transportation systems are experiencing a significant transformation due to the integration of advanced technologies, including artificial intelligence and machine learning. In the context of intelligent transportation systems (ITS) and Advanced Driver Assistance Systems (ADAS), the development of efficient and reliable traffic light detection mechanisms is crucial for enhancing road safety and traffic management. This paper presents an optimized convolutional neural network (CNN) framework designed to detect traffic lights in real-time within complex urban environments. Leveraging multi-scale pyramid feature maps, the proposed model addresses key challenges such as the detection of small, occluded, and low-resolution traffic lights amidst complex backgrounds. The integration of dilated convolutions, Region of Interest (ROI) alignment, and Soft Non-Maximum Suppression (Soft-NMS) further improves detection accuracy and reduces false positives. By optimizing computational efficiency and parameter complexity, the framework is designed to operate seamlessly on embedded systems, ensuring robust performance in real-world applications. Extensive experiments using real-world datasets demonstrate that our model significantly outperforms existing methods, providing a scalable solution for ITS and ADAS applications. This research contributes to the advancement of Artificial Intelligence-driven (AI-driven) pattern recognition in transportation systems and offers a mathematical approach to improving efficiency and safety in logistics and transportation networks.展开更多
The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converge...The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.展开更多
In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main re...In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main results generalize and extend several well-known comparable results from the existing literature.Moreover,some examples are provided to illustrate the main results.展开更多
In this paper first we prove common fixed point theorems for compatible and weakly compatible maps. Secondly, we prove common fixed point theorems for weakly compatible maps along with property (E.A.) and (CLRg) prope...In this paper first we prove common fixed point theorems for compatible and weakly compatible maps. Secondly, we prove common fixed point theorems for weakly compatible maps along with property (E.A.) and (CLRg) property respectively.展开更多
A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several exist...A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.展开更多
A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several exist...A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.展开更多
文摘Similarity relation is one of the spatial relations in the community of geographic information science and cartography.It is widely used in the retrieval of spatial databases, the recognition of spatial objects from images, and the description of spatial features on maps.However, little achievements have been made for it by far.In this paper, spatial similarity relation was put forward with the introduction of automated map generalization in the construction of multi-scale map databases;then the definition of spatial similarity relations was presented based on set theory, the concept of spatial similarity degree was given, and the characteristics of spatial similarity were discussed in detail, in-cluding reflexivity, symmetry, non-transitivity, self-similarity in multi-scale spaces, and scale-dependence.Finally a classification system for spatial similarity relations in multi-scale map spaces was addressed.This research may be useful to automated map generalization, spatial similarity retrieval and spatial reasoning.
基金The National Key Research and Development Program of China under contract No.2022YFF0801404.
文摘Ocean observations are inherently characterized by irregular temporal and spatial distributions,as well as heterogeneous spatial resolutions and error characteristics arising from the use of diverse observational platforms and techniques.To enable their application across a broad range of scientific and practical problems,it is essential to map these heterogeneous datasets into temporally and spatially consistent gridded products.Optimal Interpolation remains the most widely adopted algorithm for the mapping of oceanographic data.Two principal implementations of the optimal interpolation algorithm are commonly employed.The first,known as the basic optimal interpolation,is derived from the theory of optimal estimation and involves computationally intensive matrix operations,posing significant challenges when applied to high-dimensional problems.The second,referred to as the point-wise optimal interpolation,reduces computational complexity through point-wise estimation,thereby circumventing high-dimensional operations;however,this approach results in a substantially higher overall computational cost.In this study,a novel optimal interpolation algorithm is proposed that utilizes the Kronecker product to approximate the background error covariance matrix.This formulation enables the decomposition of high-dimensional matrix operations into smaller,computationally tractable sub-problems,thereby improving the scalability of optimal interpolation for large spatial domains with dense observational coverage.Building upon this framework,a multi-scale optimal interpolation method is further developed to enhance the integration of observational datasets with widely varying spatial resolutions,thereby improving the accuracy and applicability of the resulting gridded products.
基金funded by the Natural Science Foundation Committee,China(41364001,41371435)
文摘The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.
文摘In this paper, we discuss the relationship between k-semi-stratifiable spaces and quais-Nagata spaces and some mapping properties of quasi-Nagata spaces. We get following results: sequence-covering closed mapping preserve quasi-Nagata spaces, and finite-to-one open mappings don't preserve quasi-Nagata spaces.
基金Supported by the National Science Foundation of Yunnan Province(2 0 0 2 A0 0 58M)
文摘In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated.Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively.The results thus extend and improve some recent corresponding results.
基金Supported by the Foundation of Education Ministry of Hubei Province(D20102502)
文摘In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples.
基金Supported in part by the Foundation of Education Ministry, Anhui Province, China (No: KJ2008A028)Educa-tion Ministry, Hubei Province, China (No: D20072202)
文摘In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman＇s theorem, Roth＇s theorem and Petryshyn＇s theorem are extended to condensing mappings satisfying the interior condition.
基金supported by the National Science Fund for Distinguished Young Scholars(42225107)the National Natural Science Foundation of China(42001326,42371414,42171409,and 42271419)+1 种基金the Natural Science Foundation of Guangdong Province of China(2022A1515012207)the Basic and Applied Basic Research Project of Guangzhou Science and Technology Planning(202201011539)。
文摘Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes.In this study,we constructed a global urban structure(GUS-3D)dataset,including building volume,height,and footprint information,at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples.Our analysis indicated that the total volume of buildings worldwide in2015 exceeded 1×10^(12)m^(3).Over the 1985 to 2015 period,we observed a slight increase in the magnitude of 3D building volume growth(i.e.,it increased from 166.02 km3 during the 1985–2000 period to 175.08km3 during the 2000–2015 period),while the expansion magnitudes of the two-dimensional(2D)building footprint(22.51×10^(3) vs 13.29×10^(3)km^(2))and urban extent(157×10^(3) vs 133.8×10^(3)km^(2))notably decreased.This trend highlights the significant increase in intensive vertical utilization of urban land.Furthermore,we identified significant heterogeneity in building space provision and inequality across cities worldwide.This inequality is particularly pronounced in many populous Asian cities,which has been overlooked in previous studies on economic inequality.The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.
文摘Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.
基金Foundation items:the National Ntural Science Foundation of China(19771058)the Natural Science Foundation of Education Department of Sichuan Province(01LA70)
文摘Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.
文摘Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.
基金Supported by the Natural Science Foundation of the Educational Dept.of Zhejiang Province(20020868).
文摘This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =αnu＋（1-αn）Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.
基金Supported by the National Natural Science Foundation of China(11701245)the Scientific Research Fund of Sichuan Provincial Education Department(18ZB0272)
文摘In this article,some coupled coincidence point results for two mappings g:X→X and G:X×X→X satisfying F-contractive type conditions are obtained,and some coupled fixed point results are derived in partially ordered metric spaces.A sufficient condition for uniqueness of coupled point of coincidence are established for F type contraction,and a coupled common fixed point theorem is obtained.Some examples are given to support our results.
文摘This paper is an attempt to investigate systematically fixed points of weakly inward maps by using some basic results from differential equations in Banach spaces. By investigating the Poincare operators for such differential equations, we establish a fixed point index theory for two classes of weakly inward maps.
基金funded by the Deanship of Scientific Research at Northern Border University,Arar,Saudi Arabia through research group No.(RG-NBU-2022-1234).
文摘Transportation systems are experiencing a significant transformation due to the integration of advanced technologies, including artificial intelligence and machine learning. In the context of intelligent transportation systems (ITS) and Advanced Driver Assistance Systems (ADAS), the development of efficient and reliable traffic light detection mechanisms is crucial for enhancing road safety and traffic management. This paper presents an optimized convolutional neural network (CNN) framework designed to detect traffic lights in real-time within complex urban environments. Leveraging multi-scale pyramid feature maps, the proposed model addresses key challenges such as the detection of small, occluded, and low-resolution traffic lights amidst complex backgrounds. The integration of dilated convolutions, Region of Interest (ROI) alignment, and Soft Non-Maximum Suppression (Soft-NMS) further improves detection accuracy and reduces false positives. By optimizing computational efficiency and parameter complexity, the framework is designed to operate seamlessly on embedded systems, ensuring robust performance in real-world applications. Extensive experiments using real-world datasets demonstrate that our model significantly outperforms existing methods, providing a scalable solution for ITS and ADAS applications. This research contributes to the advancement of Artificial Intelligence-driven (AI-driven) pattern recognition in transportation systems and offers a mathematical approach to improving efficiency and safety in logistics and transportation networks.
基金Supported by the Scientific Research Fund of Sichuan Provincial Department of Science and Technology(2015JY0165,2011JYZ011)the Scientific Research Fund of Sichuan Provincial Education Department(14ZA0271)+2 种基金the Scientific Research Project of Yibin University(2013YY06)the Natural Science Foundation of China Medical University,Taiwanthe National Natural Science Foundation of China(11361070)
文摘The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.
基金Supported by the National Natural Science Foundation of China(12001249)the Natural Science Foundation of Jiangxi Province(20232BAB211004)the Educational Commission Science Programm of Jiangxi Province(GJJ2200523)。
文摘In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main results generalize and extend several well-known comparable results from the existing literature.Moreover,some examples are provided to illustrate the main results.
文摘In this paper first we prove common fixed point theorems for compatible and weakly compatible maps. Secondly, we prove common fixed point theorems for weakly compatible maps along with property (E.A.) and (CLRg) property respectively.
文摘A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.
文摘A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.
