In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings a...In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.展开更多
Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, e...Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.展开更多
In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued ...In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.展开更多
Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-value...Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.展开更多
Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in ...In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].展开更多
A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point th...A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.展开更多
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approx...We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.展开更多
A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-...A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-cooperative generalized games is proved.展开更多
SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is...SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This展开更多
Consider the continuous map f : x → X and the continuous map f of K,(X) into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of x endowed with the Hausdorff metric. ...Consider the continuous map f : x → X and the continuous map f of K,(X) into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of x endowed with the Hausdorff metric. According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli, we investigate the relations between f and f in the related dynamical properties such as transitivity, weakly mixing and mixing, etc. And by using the obtained results, we give the satisfied answers to Roman-Flores's question and Fedeli's question.展开更多
A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in...A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.展开更多
In this paper, we introduce the concepts of the conesweak subdifferential and the cone-weak direction derivative of convex set-valued mapping in a locally convex topological vector space. We study the relationship bet...In this paper, we introduce the concepts of the conesweak subdifferential and the cone-weak direction derivative of convex set-valued mapping in a locally convex topological vector space. We study the relationship between them and obtain some important results.展开更多
A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et ...A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.展开更多
A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operato...A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operator technique associated with H（·, ·）-accretivity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.展开更多
Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and di...Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and different from the corresponding known results in the literature.Some special cases of the main result are also discussed.Some examples are given to illustrate the results.展开更多
In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
基金Foundation item： Supported by the Science Foundation from the Ministry of Education of Jiangsu Province（04KJD110168, 06KJBll0107）
文摘In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.
基金the Young Foundation of Sichuan Province(06ZQ026-037) the Education Department Foundation of Sichuan Province(2005A1212006A084)
文摘Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.
基金Supported by the Science Foundation of Hangzhou Normal University（02010180）
文摘In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.
文摘Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.
文摘Fixed points for set_valued mappings from a metric space X (not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
文摘In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
基金Supported by the National Natural Science Foundation of China(No.60574073,No.10471142)
文摘In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].
基金Supported by the National Natural Science Foundation of China (No. 10771173)the Natural Science Foundation of Henan Education Department (No. 2008B110012)+1 种基金the Science and Technology Program Project of Henan Province (No. 092300410187)the Youth Foundation of Luoyang Normal University
文摘A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.
基金the Natural Science Foundation of China (No. 10471151)the Educational Science Foundation of Chongqing (KJ051307).
文摘We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.
基金the National Natural Science Foundation of China(No.10561003)
文摘A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-cooperative generalized games is proved.
文摘SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This
基金supported by the National Natural Science Foundation of China(Grant No.19971035)the Innovation Foundation of Jilin University(Grant No.2004CZ051).
文摘Consider the continuous map f : x → X and the continuous map f of K,(X) into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of x endowed with the Hausdorff metric. According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli, we investigate the relations between f and f in the related dynamical properties such as transitivity, weakly mixing and mixing, etc. And by using the obtained results, we give the satisfied answers to Roman-Flores's question and Fedeli's question.
文摘A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.
文摘In this paper, we introduce the concepts of the conesweak subdifferential and the cone-weak direction derivative of convex set-valued mapping in a locally convex topological vector space. We study the relationship between them and obtain some important results.
基金The foundation project of Chengdu University of Information Technology (No.CRF200502)
文摘A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.
基金Supported by the National Natural Science Foundation of China(Grant No.11371015)the Key Project of Chinese Ministry of Education(Grant No.211163)+3 种基金Sichuan Youth Science and Technology Foundation(GrantNo.2012JQ0032)the Foundation of China West Normal University(Grant No.11A028,11A029)the Fundamental Research Funds of China West Normal University(Grant No.13D016)the Natural Science Foundation ofSichuan Provincial Education Department(Grant No.14ZB0142)
文摘A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operator technique associated with H（·, ·）-accretivity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.
基金partially supported by NAFOSTED under Grant No.101.01-2014.17UTC under Grant No.T2017-KHCB-60
文摘Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and different from the corresponding known results in the literature.Some special cases of the main result are also discussed.Some examples are given to illustrate the results.
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
