KKM Theorems And Fixed Pixed Point Theorems In Topological Spaces

This paper mainly further studies several ocus problems of nonlinear functional analysis in generalized convex spaces,and generalizes some known results in recent literature.(1) Some fixed point theorems with weaker coercive conditions in MC-spaces are proved.These theorems include some known fixed point theorems.(2) A generalized KKM theorem is proved,and Ky Fan minimax theorem is generalized in G-convex spaces.(3) By using the better admissible class B(Y,X) and L_S-majorized mappings.FC_B -majorized mappings are introduced in FC-spaces and several existence theorems of maximal elements for FC_B-majorized mappings are proved.