A new system of the set-valued mixed quasi-variational-like inclusions (SSMQVLI) involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator tech...A new system of the set-valued mixed quasi-variational-like inclusions (SSMQVLI) involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.展开更多
In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to ...In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.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
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
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
By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion (disclu...By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion (disclusion) problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.展开更多
The authors study the existence of nontrivial solutions to p-Laplacian varia- tional inclusion systems {-△p u + |u| p-2 u ∈ 1 F (u, v), in R N , -△p v + |v| p-2 v ∈ 2 F (u, v), in R N ,where N ≥ 2, 2 ≤ p ≤ ...The authors study the existence of nontrivial solutions to p-Laplacian varia- tional inclusion systems {-△p u + |u| p-2 u ∈ 1 F (u, v), in R N , -△p v + |v| p-2 v ∈ 2 F (u, v), in R N ,where N ≥ 2, 2 ≤ p ≤ N and F : R 2 → R is a locally Lipschitz function. Under some growth conditions on F , and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.展开更多
A new system of generalized nonlinear variational-like inclusions involving Amaximal m-relaxed η-accretive(so-called,(A, η)-accretive in [36]) mappings in q-uniformly smooth Banach spaces is introduced, and then, by...A new system of generalized nonlinear variational-like inclusions involving Amaximal m-relaxed η-accretive(so-called,(A, η)-accretive in [36]) mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings due to Lan et al., the existence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings S1 and S2 and using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q =(S1, S2) which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions. The results presented in this paper extend and improve some known results in the literature.展开更多
In this paper, we introduce and study a new system of variational inclusions involving (H, η)-monotone operators in Banach space. Using the resolveut operator associated with (H, η)- monotone operators, we prove...In this paper, we introduce and study a new system of variational inclusions involving (H, η)-monotone operators in Banach space. Using the resolveut operator associated with (H, η)- monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.展开更多
基金Project supported by the Natural Science Foundation of Education Department of Sichuan Province ofChina (No. 07ZA092)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘A new system of the set-valued mixed quasi-variational-like inclusions (SSMQVLI) involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.
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 paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.
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Project supported by the Scientific Research Fund of Sichuan Normal University (No. 09ZDL04)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion (disclusion) problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.
基金Project supported by the National Natural Science Foundation of China (No. 10971194)the Zhejiang Provincial Natural Science Foundation of China (Nos. Y7080008, R6090109)the Zhejiang Innovation Project (No. T200905)
文摘The authors study the existence of nontrivial solutions to p-Laplacian varia- tional inclusion systems {-△p u + |u| p-2 u ∈ 1 F (u, v), in R N , -△p v + |v| p-2 v ∈ 2 F (u, v), in R N ,where N ≥ 2, 2 ≤ p ≤ N and F : R 2 → R is a locally Lipschitz function. Under some growth conditions on F , and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.
文摘A new system of generalized nonlinear variational-like inclusions involving Amaximal m-relaxed η-accretive(so-called,(A, η)-accretive in [36]) mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings due to Lan et al., the existence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings S1 and S2 and using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q =(S1, S2) which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions. The results presented in this paper extend and improve some known results in the literature.
基金Foundation item: the Key Project of Chinese Ministry of Education (No. 207104) the Natural Science Foundation of Hebei Province (No. A2006000941).
文摘In this paper, we introduce and study a new system of variational inclusions involving (H, η)-monotone operators in Banach space. Using the resolveut operator associated with (H, η)- monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.