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
In this paper, we are devoted to the convergence analysis of algorithms forgeneralized set-valued variational inclusions in Banach spaces. Our results improve, extend,and develop the earlier and recent corresponding r...In this paper, we are devoted to the convergence analysis of algorithms forgeneralized set-valued variational inclusions in Banach spaces. Our results improve, extend,and develop the earlier and recent corresponding results.展开更多
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
The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the diff...The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.展开更多
In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged ...In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.展开更多
The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces. By using the resolvent operator technique some existence theorem of solutions and iterative appr...The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces. By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established. The results generalize, improve and unify a number of Noor's and others' recent results.展开更多
In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its c...In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.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, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spa...In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.展开更多
Concerned with the existence and convergence properties of approximate solution to multivalued nonlinear mixed variational inclusion problem in a Hilbert space, we established the equivalence between the variational i...Concerned with the existence and convergence properties of approximate solution to multivalued nonlinear mixed variational inclusion problem in a Hilbert space, we established the equivalence between the variational inclusion and the general resolvent equations, obtained three iterative algorithms, provided the convergence analysis of the algorithms. The results obtained improve and generalize a number of resent results.展开更多
The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent res...The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results.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
We discuss the set-valued dynamics related to the theory of functional equations.We look for selections of convex set-valued functions satisfying set-valued Euler-Lagrange inclusions.We improve and extend upon some of...We discuss the set-valued dynamics related to the theory of functional equations.We look for selections of convex set-valued functions satisfying set-valued Euler-Lagrange inclusions.We improve and extend upon some of the results in[13,20],but under weaker assumptions.Some applications of our results are also provided.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
A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven tha...A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.展开更多
This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Ca...This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].展开更多
In this paper, we posed a random iterative algorithm for generalized multivalued random variational like inclusions. We define the random relaxed Lipschitz and relaxed monotone mappings and prove the existence and con...In this paper, we posed a random iterative algorithm for generalized multivalued random variational like inclusions. We define the random relaxed Lipschitz and relaxed monotone mappings and prove the existence and convergence of solutions of the random iterative sequences generated by a random iterative algorithm.展开更多
In this paper,we consider system of variational inclusions and its several spacial cases,namely,alternating point problems,system of variational inequalities,etc.,in the setting of Hadamard manifolds.We propose an ite...In this paper,we consider system of variational inclusions and its several spacial cases,namely,alternating point problems,system of variational inequalities,etc.,in the setting of Hadamard manifolds.We propose an iterative algorithm for solving system of variational inclusions and study its convergence analysis.Several special cases of the proposed algorithm and convergence result are also presented.We present application to constraints minimization problems for bifunctions in the setting of Hadamard manifolds.At the end,we illustrate proposed algorithms and convergence analysis by a numerical example.The algorithms and convergence results of this paper either improve or extend known algorithms and convergence results from linear structure to Hadamard manifolds.展开更多
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This subject is supported both by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Educations of MOE,P.R.C.,and by the National Natural Science Foundation of China(19801023)
文摘In this paper, we are devoted to the convergence analysis of algorithms forgeneralized set-valued variational inclusions in Banach spaces. Our results improve, extend,and develop the earlier and recent corresponding results.
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Project supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of Ministry of Education, China (No.0705)the Dawn Program Fund of Shanghai of China (No.BL200404)Shanghai Leading Academic Discipline Project (No.T0401)
文摘The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.
文摘In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.
文摘The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces. By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established. The results generalize, improve and unify a number of Noor's and others' recent results.
文摘In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.
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Project supported by the National Natural Science Foundation of China (No. 10671135)the Key Program of the National Natural Science Foundation of China (No. 70831005)the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20060610005)
文摘In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.
文摘Concerned with the existence and convergence properties of approximate solution to multivalued nonlinear mixed variational inclusion problem in a Hilbert space, we established the equivalence between the variational inclusion and the general resolvent equations, obtained three iterative algorithms, provided the convergence analysis of the algorithms. The results obtained improve and generalize a number of resent results.
文摘The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results.
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.
文摘We discuss the set-valued dynamics related to the theory of functional equations.We look for selections of convex set-valued functions satisfying set-valued Euler-Lagrange inclusions.We improve and extend upon some of the results in[13,20],but under weaker assumptions.Some applications of our results are also provided.
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 Key Program of National Natural Science Foundation of China(No.70831005)the National Natural Science Foundation of China(No.10671135)the Fundamental Research Funds for the Central Universities(No.2009SCU11096)
文摘A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.
文摘This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].
文摘In this paper, we posed a random iterative algorithm for generalized multivalued random variational like inclusions. We define the random relaxed Lipschitz and relaxed monotone mappings and prove the existence and convergence of solutions of the random iterative sequences generated by a random iterative algorithm.
文摘In this paper,we consider system of variational inclusions and its several spacial cases,namely,alternating point problems,system of variational inequalities,etc.,in the setting of Hadamard manifolds.We propose an iterative algorithm for solving system of variational inclusions and study its convergence analysis.Several special cases of the proposed algorithm and convergence result are also presented.We present application to constraints minimization problems for bifunctions in the setting of Hadamard manifolds.At the end,we illustrate proposed algorithms and convergence analysis by a numerical example.The algorithms and convergence results of this paper either improve or extend known algorithms and convergence results from linear structure to Hadamard manifolds.
