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
We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty ...We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.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
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
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 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, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-so...In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P. Aubin et al. are generalized and improved.展开更多
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded...The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space.展开更多
This paper deals with the monotone iterative method for set -- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontin...This paper deals with the monotone iterative method for set -- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontinuous nonlinear differential equation problem is discussed.展开更多
The existence of continuous solutions for fractional integral inclusion via its singlevalued problem and fixed point theorem for set-valued function in locally convex topological spaces is discussed. The proof of the ...The existence of continuous solutions for fractional integral inclusion via its singlevalued problem and fixed point theorem for set-valued function in locally convex topological spaces is discussed. The proof of the single-valued problem will be based on the Leray- Schauder fixed point theorem. Moreover, the controllability of this solution is studied.展开更多
In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a resul...In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a result about integrability of products of the form gοf.f'f(k)under suitable mild conditions and, finally, we prove that a Nemytskij operator Sg maps BV''[a,b] a distinguished subspace of the space of all functions of second bounded variation, into itself if, and only if, g BV''loc(R) A similar result is obtained for the space of all functions of bounded (p,2)-variation (1≤p≤1),展开更多
In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further,...In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.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.
文摘We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.
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.
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.
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.
文摘In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P. Aubin et al. are generalized and improved.
基金the the Morningside Center of Mathematics of the Chinese Academy of Sciencesthe Program of "One Hundred Distinguished Chinese Scientists" of the Chinese Academy of Sciences.
文摘The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space.
基金the National Natural Sciences Foundation of China
文摘This paper deals with the monotone iterative method for set -- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontinuous nonlinear differential equation problem is discussed.
文摘The existence of continuous solutions for fractional integral inclusion via its singlevalued problem and fixed point theorem for set-valued function in locally convex topological spaces is discussed. The proof of the single-valued problem will be based on the Leray- Schauder fixed point theorem. Moreover, the controllability of this solution is studied.
文摘In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a result about integrability of products of the form gοf.f'f(k)under suitable mild conditions and, finally, we prove that a Nemytskij operator Sg maps BV''[a,b] a distinguished subspace of the space of all functions of second bounded variation, into itself if, and only if, g BV''loc(R) A similar result is obtained for the space of all functions of bounded (p,2)-variation (1≤p≤1),
基金Supported by the Natural Science Foundation of Guizhou university(200101007)
文摘In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.
