The Existence Of Fixed Point Theorems

The paper mainly studies the existence of the fixed points of many kinds of mappings.The first chapter as an introduction, Introducing the fixed point of the development ofthe theory of background and the present situation,giving the research work and results ofthis paper.In the second chapter,introducing a new method to show the existence of fixed pointfor nonexpansive mappings defined on closed,convex not necessarily bounded subsets ofBanach spaces,using Hausdorff measure of noncompactness throughout this paper.In the third chapter, giving a definition called locally (D) property which imply theexistence of fixed point theorems for multivalued nonexpansive mappings.Then, giving amapping called α-nonexpansive mappings and obtain fixed point theorem under the condi-tions of locally (D).In the forth chapter, giving a definition of a new kind of mapping which related with themapping satisfying C condition,discussing and obtaining the convergence theorems andthe existence of fixed point theorems.Finally, the conclusion is showed in the fifth chapter, and some problems we need studylater are given.