In this paper, we introduce the concepts of weakly R-KKM mappings, R- convex and R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topolo...In this paper, we introduce the concepts of weakly R-KKM mappings, R- convex and R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan＇s matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.展开更多
In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence th...In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence theorems.matching theorems and vector valued minimax inequalities which generalize slightly thecorresponding results in[1,2,4,5,6,7].展开更多
In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational ineq...In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10471113)the Natural Science Foundation of Chongqing Municipal Commission of Science and Technology (N0.2005BB2097)
文摘In this paper, we introduce the concepts of weakly R-KKM mappings, R- convex and R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan＇s matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.
文摘In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence theorems.matching theorems and vector valued minimax inequalities which generalize slightly thecorresponding results in[1,2,4,5,6,7].
文摘In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.
