Fc-space Intersection Theorem And Its Applications

This thesis consists of five chapters. At first, the concept of finite continuous topological space without convexity structure and linear structure are introduced. Secondly, Ky Fan type coincidence theorems and alternative theorems of variational inequality are obtained on the basis of classical KKM theorem in FC-spaces. And then, some intersection theorems are obained. Further, Systems of Fan type inequalies for families of real-valued mapping defined on noncompact product FC-spaces are obained by Using known results of intersection theorems. Finally, some Von Newmann type alternative theorems and Von Newmann-sion type minimax inequality theorems are given as application of theorems above.This thesis enriches the study results on intersection theory and intersection theory can be studied and applied more widely.