Convergence Of The Fixed Point Iterative Approximation For Several Types Of Operators

Receiving the attention by many scholars,the study of the fixed point theory has become a hot topic of nonlinear analysis and application.Improving some conditions,some scholars have generalized the metric space and gotten numerous good results.These results have wide applications in different fields.This article mainly studies the existence and uniqueness of the fixed point for several types of mappings in the G-metric space and S-metric space,and weak convergence of nonexpansive semigroup in the uniformly convex Banach Spaces.There are four chapters in this thesis as following:In chapter one,we mainly introduce the relevant knowledge background and the research current situation as well as the research significance of the fixed point theorem.The research content of this paper is also illustrated briefly.In chapter two,firstly,we study the existence and uniqueness of the fixed point for some expansive mappings and the common fixed point for expansive mapping pairs in the G-metric spaces.Then the common fixed point theorem of (?,?)-expansive mapping is obtained by discussing the two compatible mappings in the G-metric space.In chapter three,we mainly study the existence and uniqueness of four common fixed points of self-mapping with the ?-compression condition in the S-metric space.Then we introduce the concept of compatible mapping in the partially ordered S-metric space.And some coupled coincidence point and some common coupled fixed point theorems for compatible mappings are achieved.In chapter four,we mainly study the existence problem of an implicit iterative sequence{X_n}by using iterative approximation method.A weak convergence theorem is established for the nonexpansive semigroup ?={T(t):0?t??} in uniformly convex Banach spaces without the Opial property.