By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence re...By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equi...By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.展开更多
In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are...In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.展开更多
In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci(x)-FC-partially diagonally quasico...In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci(x)-FC-partially diagonally quasiconvex, Ci(x)-FC-quasiconvex, and Ci(x)-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.展开更多
A new bilevel generalized mixed equilibrium problem (BGMEF) is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the ...A new bilevel generalized mixed equilibrium problem (BGMEF) is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field.展开更多
A new system of vector quasi-equilibrium problems is introduced and its existence of solution is proved. As applications, some existence results of weak Pareto equilibrium for both constrained multicriteria games and ...A new system of vector quasi-equilibrium problems is introduced and its existence of solution is proved. As applications, some existence results of weak Pareto equilibrium for both constrained multicriteria games and multicriteria games without constrained correspondences are also shown.展开更多
A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is intro...A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.展开更多
In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-...In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.展开更多
In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters a...In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.展开更多
A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalize...A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.展开更多
The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for ...The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.展开更多
In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseu...In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].展开更多
A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for sol...A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.展开更多
In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of non...In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions.展开更多
In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener...In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.展开更多
Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector...Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.展开更多
By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the ge...By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature.展开更多
A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium pro...A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem (AMEP) is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems (SGEP) is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.展开更多
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金Supported by NSF of Chongqing and Science Foundations of Chongqing Jia1otong University
文摘By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金This project was supported by the NSF of Sichuan Education of China(2003A081)and SZD0406
文摘By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.
基金supported by the National Science Foundation of China and Shanghai Pujian Program
文摘In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.
基金supported by the Scientific Research Fun of Sichuan Normal University (09ZDL04)the Sichuan Province Leading Academic Discipline Project (SZD0406)
文摘In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci(x)-FC-partially diagonally quasiconvex, Ci(x)-FC-quasiconvex, and Ci(x)-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.
基金Project 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 bilevel generalized mixed equilibrium problem (BGMEF) is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field.
基金Project supported by the National Natural Science Foundation of China (Nos.10171118 and 70432001) the Applied Basic Research Foundation of Chongqing(No.030801) the Natural Science Foundation of Chongqing(No.8409) and the Postdoctoral Science Foundation of China
文摘A new system of vector quasi-equilibrium problems is introduced and its existence of solution is proved. As applications, some existence results of weak Pareto equilibrium for both constrained multicriteria games and multicriteria games without constrained correspondences are also shown.
基金Project supported by the Scientific Research Fund of Sichuan Normal University(No.09ZDL04)the Sichuan Province Leading Academic Discipline Project(No.SZD0406)
文摘A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.
基金supported by the Natural Science Foundation of Sichuan Education Department of China(No. 07ZA092)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.
基金The NSF(10871226) of Chinathe NSF(ZR2009AL006) of Shandong Province
文摘In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.
基金supported by the Scientific Research Fund of Sichuan Normal University (No.09ZDL04)the Sichuan Province Leading Academic Discipline Project (No.SZD0406)
文摘A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.
文摘The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.
基金supported by Scientific Research Fund of Sichuan Provincial Education Department (09ZB102)Scientific Research Fund of Science and Technology Deportment of Sichuan Provincial (2011JYZ011)
文摘In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].
基金supported by the Scientific Research Fun of Sichuan Normal University (11ZDL01)the Sichuan Province Leading Academic Discipline Project (SZD0406)
文摘A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.
文摘In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions.
文摘In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.
文摘Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.
基金Project supported by the Key Program of the National Natural Science Foundation of China(NSFC)(No.70831005)the National Natural Science Foundation of China(Nos.11171237,11226228,and 11201214)+1 种基金the Science and Technology Program Project of Henan Province of China(No.122300410256)the Natural Science Foundation of Henan Education Department of China(No.2011B110025)
文摘By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature.
基金Project supported by the Sichuan Province Leading Academic Discipline Project(No.SZD0406)the Scientific Research Fund of Sichuan Normal University(No.11ZDL01)
文摘A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem (AMEP) is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems (SGEP) is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.