Research On Some Problems Of Nonlinear Operator Equations In Generalized Metric Spaces

This paper created GL-metric spaces,and studied the existence problem of solutions of different nonlinear operator equations in partially ordered complexvalued Gb-metric spaces,GL-metric spaces and generalized F-metric spaces.At the same time,we have been obtained several theorems,examples and applications through research.This paper is divided into five chapters.In the first chapter,the historical background and development status of fixed point theory of nonlinear operators are introduced,and some basic concepts of generalized metric spaces are given.In the second chapter,we propose some new concepts of the complex valued CP-class function,a type of Geraghty contraction and a type of JS contraction respectively,prove three existence theorems of solutions of nonlinear operator equations in partially ordered complex-valued Gb-metric spaces,and also we give some examples to support main results.In the third chapter,we establish the GL-metric spaces,propose some new concepts of a type of cyclic GL-Geraghty-contractive mapping,a type of cyclic GLJS-contractive mapping and a type of cyclic GL-φ-contractive mapping respectively,prove three existence theorems of solutions of nonlinear operator equations in this space.Moreover,we also provided some examples and specific application.In the fourth chapter,we propose a new concept of multi-valued mappings with the greatest lower bound property in generalized F-metric spaces,study the problem of common solution of nonlinear operator equations,and establish some existence theorems of solutions of other nonlinear operator equations via more general contractions.On the other hand,we have obtained several new corollaries and application.In the fifth chapter,we summarize the research work and innovation of this paper,and make further prospects for the theoretical research on solutions of nonlinear operator equations.