In the present paper there are given a number of minimax-type inequalities for a family of functions,involving two multivalued mappings,one being strongly decomposable and the other monotone.Hence some applications to...In the present paper there are given a number of minimax-type inequalities for a family of functions,involving two multivalued mappings,one being strongly decomposable and the other monotone.Hence some applications to the variational-type inequality theory and to the fixed point theory.展开更多
As important applications of minimax-type inequalities for a family of functions in [3], in the present paper there are given a number of existence theorems on simultaneous solutions to fixed point and minimax-type in...As important applications of minimax-type inequalities for a family of functions in [3], in the present paper there are given a number of existence theorems on simultaneous solutions to fixed point and minimax-type inequality problems and to fixed point and variational-type inequality problems. not only abolishing the paracompactness hypothesis on the underlying space and weak- ening the others in the results in[1], but also making them still nicer in form with still more concise and straightforward proofs.展开更多
Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related gen...Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.展开更多
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t...The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.展开更多
In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity s...In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.展开更多
基金Supported both by the National Natural Science Foundation of China and by the Institute of Mathematics,Academia Sinica
文摘In the present paper there are given a number of minimax-type inequalities for a family of functions,involving two multivalued mappings,one being strongly decomposable and the other monotone.Hence some applications to the variational-type inequality theory and to the fixed point theory.
基金Supported both by the National Natural Science Foundation of Chinaby the Institute of Mathematics. Academia Sinica
文摘As important applications of minimax-type inequalities for a family of functions in [3], in the present paper there are given a number of existence theorems on simultaneous solutions to fixed point and minimax-type inequality problems and to fixed point and variational-type inequality problems. not only abolishing the paracompactness hypothesis on the underlying space and weak- ening the others in the results in[1], but also making them still nicer in form with still more concise and straightforward proofs.
文摘Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.
文摘The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.
基金This project is supported by Natural Science Foundation of Sichuan Education Department of China(2003A081)SZD0406
文摘In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.
