Research On Some Nonlinear Operator Problems In Generalized Metric Spaces

Nonlinear operator theory is one of the main contents of nonlinear functional analysis,in which the study of fixed points and coincidence points of nonlinear operators is particularly important and widely used.With the further study of the fixed point theory,scholars began to try to introduce different contractive mappings in all kinds of spaces,and to study whether there is a unique fixed point with these mappings.This paper mainly studies some problems of G-metric spaces,b-metric spaces,Gb-metric spaces and partially metric spaces,and discusses the coincidence point,fixed point,common fixed point and coupled common fixed point problems in these four spaces.This paper can be divided into six chapters.In Chapter one,we introduce the historical background and development status of fixed point problems in generalized metric spaces,and give the related concepts needed in the following chapters.In Chapter two,we prove the coincidence point theorems in C-metric spaces and common fixed point theorems under weakly compatible conditions.In Chapter three,we introduce Meir-Keeler function to study the fixed point problems under new conditions in b-metric spaces.In Chapter four,we study the existence and uniqueness of the coupled common fixed point under new contractive conditions for three self-mappings in Gb-metric spaces.In Chapter five,we use the mixed g-monotone property of mappings and establish new contractive conditions in partially ordered metric spaces to prove the coupled coincidence point theorems and coupled common fixed point theorems for two mappings.In Chapter six,the conclusions of this paper are summarized and prospected.