Iterative Methods For Fixed Points Of Operators In Cone 2-metric Spaces And Banach Spaces

This paper discusses the existence and uniqueness of fixed points of several different types of mappings in cone 2-metric spaces,and the approximation iterative methods of nonexpansive mappings in Banach spaces.The paper is divided into three chapters,mainly as follows:The first chapter introduces the background of the fixed point theorem.Then,some newer research results of the fixed point theorem are introduced.Finally,the research content of this paper is introduced.In the second chapter,the cone 2-metric space of Banach algebra is briefly introduced as a generalization of the cone metric space and some lemmas related to the main results are given.Secondly,in the cone 2-metric space of Banach algebra,the existence and uniqueness of the fixed points of exchangeable mapping pairs with inclusion relations are investigated.Then,the four common fixed point theorems with weak compatible relational mapping are studied,and the operation of taking the minimum between the two is introduced to obtain the inference result.After that,it is extended to three maps with weak compatible relations,and the unique points of the fixed points are studied.Finally,the common fixed points of the two mapping families are studied and extended to several different situations.As a theoretical basis for the application,a concrete example is given.In the third chapter,the generalized viscous iterative methods for infinite family nonexpansive mappings are introduced and analyzed.Then,the generalized viscous iterative method can be used to make infinite family non-expansive mappings in reflexive smooth convex Banach.The conclusion that the space strongly converges to a common fixed point,and also solves some variational inequalities.