In this paper,we introduce some ideal-derived-set mappings in uniform spaces and investigate the images of those mappings.Meanwhile,we introduce a concept of I-Hurewicz boundedness,study some basic topological operati...In this paper,we introduce some ideal-derived-set mappings in uniform spaces and investigate the images of those mappings.Meanwhile,we introduce a concept of I-Hurewicz boundedness,study some basic topological operations of them.Finally,we obtain an equivalent characterization of I-Hurewicz boundedness in uniform spaces.展开更多
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this pap...Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of Π_(C).We investigate some properties of the Gâteaux directional differentiability of Π_(C).In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of Π_(C).By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator Π_(C) and the Gâteaux directional derivatives of the standard metric projection operator PC.展开更多
In this paper, we attempt to give a unified approach to the existing several versions of Ekeland＇s variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances....In this paper, we attempt to give a unified approach to the existing several versions of Ekeland＇s variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances. Then we introduce a new type of completeness for uniform spaces, i.e., sequential completeness with respect to a q-distance （particularly, a p-distance）, which is a very extensive concept of completeness. By using q-distances and the new type of completeness, we prove a generalized Takahashi＇s nonconvex minimization theorem, a generalized Ekeland＇s variational principle and a generalized Caristi＇s fixed point theorem. Moreover, we show that the above three theorems are equivalent to each other. From the generalized Ekeland＇s variational principle, we deduce a number of particular versions of Ekeland＇s principle, which include many known versions of the principle and their improvements.展开更多
In this paper,we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces.We introduce the concept of topological stability for homeomorphisms on compact uniform spa...In this paper,we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces.We introduce the concept of topological stability for homeomorphisms on compact uniform spaces and prove that if a homeomorphism on a compact uniform space is expansive and has pseudo-orbit tracing property,then it is topologically stable.Moreover,we discuss the topological stability for homeomorphisms on uniform spaces from the view of localization.We introduce definitions of topologically stable point and shadowable point for homeomorphisms on uniform spaces and show that every shadowable point of an expansive homeomorphism on a compact uniform space is topologically stable.展开更多
Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical meth...Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.展开更多
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of thre...In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.展开更多
In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-...In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-η-monotone opera- tors, we prove the approximation solvability of solutions using an iterative algorithm. The results in this paper extend and improve some known results from the literature.展开更多
In this paper,the author proves that if the dual X^(*)of X is weakly locally uniformly convex and the convex function f is continuous on X,then there exist two sequences{f_(n)}_(n=1)^(∞)and{g_(n)}_(n=1)^(∞)of contin...In this paper,the author proves that if the dual X^(*)of X is weakly locally uniformly convex and the convex function f is continuous on X,then there exist two sequences{f_(n)}_(n=1)^(∞)and{g_(n)}_(n=1)^(∞)of continuous functions on X^(**)such that(1)f_(n)(x)≤f_(n+1)(x)≤f(x)≤g_(n+1)(x)≤g_(n)(x)whenever x∈X;(2)the two convex functions f_(n)and g_(n)are Gâteaux differentiable on X;(3)f_(n)→f and g_(n)→f uniformly on X.Moreover,if the function f is coercive on X,then(1)f_(n)and g_(n)are two w^(*)-lower semicontinuous convex functions on X^(**);(2)epif_(n)=epif_(n)∩(X×R)^(w)^(*)andg_(n)=epig_(n)∩(X×R)^(w)^(*).展开更多
In this article, we show that the universal covering of any complete normal Kähler space of constant holomorphic sectional curvature on the regular locus is exactly biholomorphic to one of the complex projective ...In this article, we show that the universal covering of any complete normal Kähler space of constant holomorphic sectional curvature on the regular locus is exactly biholomorphic to one of the complex projective space, the complex Euclidean space or the complex Euclidean ball. Moreover, we also prove that in a normal Stein space any bounded domain with complete Bergman metric of constant holomorphic sectional curvature on the regular locus is necessarily biholomorphic to the complex Euclidean ball, by which we generalize the classical Lu Qi-Keng uniformization theorem to the singular setting.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
Currently,polarization visualization strategies are accomplished by mapping polarization information into a perceptually uniform color appearance model CAM02-UCS.However,the deviation of the CAM02-UCS space from the l...Currently,polarization visualization strategies are accomplished by mapping polarization information into a perceptually uniform color appearance model CAM02-UCS.However,the deviation of the CAM02-UCS space from the lightness prediction results in an inaccurate match between the polarization information and the perceptual information.In this paper,we propose a novel polarization visualization strategy based on the perceptual uniform space Jzazbz.The polarization visualization be completed by placing the polarization information into the lightness Jz,colorfulness Cz and hue angle hz channels of the Jzazbz space.The experimental results show that the proposed method can significantly improve the lightness of the low irradiance and high polarization region,hence more polarization information can be sensed by human visual system.展开更多
The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in...The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.展开更多
A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate...A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces.展开更多
Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is ...Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.展开更多
This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces. In this paper, the uniformity and properties far generalized H-space are con...This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces. In this paper, the uniformity and properties far generalized H-space are considered. The conditions of metrization and the form of metric functions for generalized H-spaces, H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented. The results of this paper generalize and unify some recent results of [1-2, 8, 10].展开更多
This paper investigates the formation control of a class of multi-agent systems moving on a circle, whose topology is a cyclic graph, and presents several new results for the following two cases: Case I, the agents wi...This paper investigates the formation control of a class of multi-agent systems moving on a circle, whose topology is a cyclic graph, and presents several new results for the following two cases: Case I, the agents with single-integrator kinematics,and Case II, the agents with double-integrator kinematics. Firstly,for Case I, two control protocols are proposed under which the multiagent systems keep a uniformly-spaced formation. Secondly,we study Case II, and a control protocol is designed for this case, then the stability of the formation is proved. Finally, three simulations are studied by using our presented results. The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying the formation control of this class of multi-agent systems.展开更多
In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive...In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.展开更多
This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several not...This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.展开更多
In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transf...In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.展开更多
A 300 μm×300 μm light emitting diode(LED) chip is divided into nine 80 μm×80 μm units with 30 μm spacing between adjacent ones. After arraying, the total saturation light output power and the maximum in...A 300 μm×300 μm light emitting diode(LED) chip is divided into nine 80 μm×80 μm units with 30 μm spacing between adjacent ones. After arraying, the total saturation light output power and the maximum injection current are enhanced by 5.19 times and nearly 7 times, respectively. In addition, the test results demonstrate that the illuminance uniformity on the receiving surface reaches the optimum when the spacing between the arrays is equal to the maximum flat condition. The larger the number of arrays, the greater the area with uniform illuminance on the receiving surface.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12171015)the Natural Science Foundation of Fujian Province(Grant Nos.2023J011078+1 种基金2020J05230)the Project of Innovation Groups of Ningde Normal University(Grant No.2023T01)。
文摘In this paper,we introduce some ideal-derived-set mappings in uniform spaces and investigate the images of those mappings.Meanwhile,we introduce a concept of I-Hurewicz boundedness,study some basic topological operations of them.Finally,we obtain an equivalent characterization of I-Hurewicz boundedness in uniform spaces.
文摘Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of Π_(C).We investigate some properties of the Gâteaux directional differentiability of Π_(C).In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of Π_(C).By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator Π_(C) and the Gâteaux directional derivatives of the standard metric projection operator PC.
基金Supported by National Natural Science Foundation of China(Grant No.10871141)
文摘In this paper, we attempt to give a unified approach to the existing several versions of Ekeland＇s variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances. Then we introduce a new type of completeness for uniform spaces, i.e., sequential completeness with respect to a q-distance （particularly, a p-distance）, which is a very extensive concept of completeness. By using q-distances and the new type of completeness, we prove a generalized Takahashi＇s nonconvex minimization theorem, a generalized Ekeland＇s variational principle and a generalized Caristi＇s fixed point theorem. Moreover, we show that the above three theorems are equivalent to each other. From the generalized Ekeland＇s variational principle, we deduce a number of particular versions of Ekeland＇s principle, which include many known versions of the principle and their improvements.
基金Supported by NNSF of China(Grant Nos.11861010,11761012)NSF for Distinguished Young Scholar of Guangxi Province(Grant No.2018GXNSFFA281008)+2 种基金supported by the Cultivation Plan of Thousands of Young Backbone Teachers in Higher Education Institutions of Guangxi ProvinceProgram for Innovative Team of Guangxi University of Finance and EconomicsProject of Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing(Grant No.201801ZZ03)。
文摘In this paper,we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces.We introduce the concept of topological stability for homeomorphisms on compact uniform spaces and prove that if a homeomorphism on a compact uniform space is expansive and has pseudo-orbit tracing property,then it is topologically stable.Moreover,we discuss the topological stability for homeomorphisms on uniform spaces from the view of localization.We introduce definitions of topologically stable point and shadowable point for homeomorphisms on uniform spaces and show that every shadowable point of an expansive homeomorphism on a compact uniform space is topologically stable.
文摘Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.
文摘In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.
基金The NSF(60804065)of Chinathe Foundation(11A028)of China West Normal University
文摘In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-η-monotone opera- tors, we prove the approximation solvability of solutions using an iterative algorithm. The results in this paper extend and improve some known results from the literature.
基金supported by the National Natural Science Foundation of China(No.12271121).
文摘In this paper,the author proves that if the dual X^(*)of X is weakly locally uniformly convex and the convex function f is continuous on X,then there exist two sequences{f_(n)}_(n=1)^(∞)and{g_(n)}_(n=1)^(∞)of continuous functions on X^(**)such that(1)f_(n)(x)≤f_(n+1)(x)≤f(x)≤g_(n+1)(x)≤g_(n)(x)whenever x∈X;(2)the two convex functions f_(n)and g_(n)are Gâteaux differentiable on X;(3)f_(n)→f and g_(n)→f uniformly on X.Moreover,if the function f is coercive on X,then(1)f_(n)and g_(n)are two w^(*)-lower semicontinuous convex functions on X^(**);(2)epif_(n)=epif_(n)∩(X×R)^(w)^(*)andg_(n)=epig_(n)∩(X×R)^(w)^(*).
基金supported by the National Key R&D Program of China(Grant No.2021YFA1002600)NSFC(Grant No.12201060)。
文摘In this article, we show that the universal covering of any complete normal Kähler space of constant holomorphic sectional curvature on the regular locus is exactly biholomorphic to one of the complex projective space, the complex Euclidean space or the complex Euclidean ball. Moreover, we also prove that in a normal Stein space any bounded domain with complete Bergman metric of constant holomorphic sectional curvature on the regular locus is necessarily biholomorphic to the complex Euclidean ball, by which we generalize the classical Lu Qi-Keng uniformization theorem to the singular setting.
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This work was supported by the Key Research and Development Program of Shaanxi(2018ZDXM-GY-091)the National Key Research and Development Project of China(2018YFB1309403)+2 种基金the Natural National Science Foundation of China(61805199)Natural Science Basic Research Plan in Shaanxi Province of China(2018JQ6065)We would like to sincerely thank all reviewers for their helpful comments and suggestions.
文摘Currently,polarization visualization strategies are accomplished by mapping polarization information into a perceptually uniform color appearance model CAM02-UCS.However,the deviation of the CAM02-UCS space from the lightness prediction results in an inaccurate match between the polarization information and the perceptual information.In this paper,we propose a novel polarization visualization strategy based on the perceptual uniform space Jzazbz.The polarization visualization be completed by placing the polarization information into the lightness Jz,colorfulness Cz and hue angle hz channels of the Jzazbz space.The experimental results show that the proposed method can significantly improve the lightness of the low irradiance and high polarization region,hence more polarization information can be sensed by human visual system.
文摘The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.
基金supported by the Scientific Research Fund of Sichuan Normal University(No.11ZDL01)the Sichuan Province Leading Academic Discipline Project(No.SZD0406)
文摘A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces.
基金National Natural Science Foundations of China(No.10901033,No.10971023)Shanghai Pujiang Project,China(No.08PJ1400600)+1 种基金Shanghai Shuguang Project,China(No.07SG38)the Fundamental Research Funds for the Central Universities of China
文摘Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.
文摘This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces. In this paper, the uniformity and properties far generalized H-space are considered. The conditions of metrization and the form of metric functions for generalized H-spaces, H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented. The results of this paper generalize and unify some recent results of [1-2, 8, 10].
基金supported by the National Natural Science Foundation of China(G61374065,61373081,61303007,61401260,61503225,61572298)the Research Fund for the Taishan Scholar Project of Shandong Province of Chinathe Natural Science Foundation of Shandong Province(ZR2015FQ003)
文摘This paper investigates the formation control of a class of multi-agent systems moving on a circle, whose topology is a cyclic graph, and presents several new results for the following two cases: Case I, the agents with single-integrator kinematics,and Case II, the agents with double-integrator kinematics. Firstly,for Case I, two control protocols are proposed under which the multiagent systems keep a uniformly-spaced formation. Secondly,we study Case II, and a control protocol is designed for this case, then the stability of the formation is proved. Finally, three simulations are studied by using our presented results. The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying the formation control of this class of multi-agent systems.
文摘In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
基金Supported b-y National Natural Science Foundation of China （Grant No. 10926042 and 11001231）, China Postdoctoral Science Foundation （Grant No. 20090460356）, RFDP （Grant No. 200803841018）Acknowledgements The authors would like to thank Professor Cheng Lixin and Professor Bu Shangquan for many helpful conversations on this paper, and also thank the referee for many valuable suggestions.
文摘This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.
文摘In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(No.61204055)
文摘A 300 μm×300 μm light emitting diode(LED) chip is divided into nine 80 μm×80 μm units with 30 μm spacing between adjacent ones. After arraying, the total saturation light output power and the maximum injection current are enhanced by 5.19 times and nearly 7 times, respectively. In addition, the test results demonstrate that the illuminance uniformity on the receiving surface reaches the optimum when the spacing between the arrays is equal to the maximum flat condition. The larger the number of arrays, the greater the area with uniform illuminance on the receiving surface.
