The Study Of Problems On The Existence And Uniqueness Of Common Fixed Point For Several Classes Operators

The existence and uniqueness of fixed point problem for multiple mappings on metric spaces, numerous mathematical author have established a series of famous results. The study of this paper involves fixed point theorems for a generalized metric space, a multiplicative metric space and a partial metric space. In particular, we also discussed the coupled coin-cidence point and common coupled fixed point problem. The purpose of this paper is to extend the existing results on more extensive metric spaces, and study the common fixed point problems for generalizing mappings by introducing new concepts, new methods. So the significance of this study is very important.This paper is divided into four chapters.In chapter 1. we introduced the research background and current situation analysis of fixed point theory and coupled fixed point theory on generalized metric space and partial metric space.In chapter 2, In chapter 2, we discuss the common fixed point problem for three pairs self-maps on generalized metric space. With only two pairs self-maps satisfying the common (E.A) property, we prove a new common fixed point theorem for three pairs self-maps. An example is provided to support our new result. The result obtained in this paper differ from the recent relative results in the literature.In chapter 3, by using the concept of weakly commutative mappings for self-maps pairs in multiplicative metric space, we prove some new common fixed point theorems for two pairs self-maps.In chapter 4, we prove some common fixed point theorems for two pairs of weakly com-patible self-maps satisfying a new ψ-type contractive condition in the framework of a partial metric space. We also provide illustrative examples in support of our new results.In chapter 5, we establish some new coupled coincidence point and common coupled fixed point theorems for nonlinear mappings defined on a set equipped with two quasi-partial b-metrics. In addition, we also provide an usability example to illustrate our new results.