The Study Of Problems On Fixed Point And Coupled Fixed Point For Several Classes Nonlinear Operators

The problems on the existence and uniqueness of fixed point for multiple operators on metric spaces,and coupled fixed point of multivariate function have been studied by mathematical author,which have received a series of significant research.The study of this paper involves some widely space types,such as S-metric space,b-metric space and rectangular b-metric space etc.We mainly discussed the coupled coincidence point and common coupled fixed point problem for some operators on such spaces.The purpose of this paper is to study the common fixed point and coupled fixed point problems for generalizing mappings by introducing new concepts and new methods.The results of this paper essentiallyextend and promote the existing results on more extensive metric spaces such as S-metric space,b-metric space and rectangular b-metric space.So the theoretical significance and application value 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 common fixed point theory and coupled fixed point theory for nonlinear mappings on S-metric space,b-metric space,multiplicative space,2-metric space and rectangular b-metric space.In chapter 2,we discuss a new class of contractive condition and study the existence and uniqueness of couple coincidence point and couple common fixed point problem on two S-metric spaces which defined on a set.We prove a new common coupled fixed point theorems.Two numerical examples are provided to support our new result effectively.We also give an existence and uniqueness of solution for some class of nonlinear integral equations,as the application of the obtained result.In chapter 3,by using the concept of weakly compatible and compatible mappings we discuss common fixed point problems for six self-mapping pairs in complete b-metric space,we prove some new common fixed point theorems.Two numerical examples are provided to support our new result effectively.In chapter 4,we discuss couple coincidence point and couple common fixed point theorem by establishing a new(?,?)-type contractive condition in the frame-work of rectangular b-space.We also provide practical examples in support of our new results.At last,We prove the existence of solution for some class of nonlinear integral equations,by using the new obtained result.