Fixed Point Theorems For A Class Of Decreasing Operators

Fixed point theorem is one of the important methods to study the existence and uniqueness of solutions of differential integral equations.With the development of nonlinear science,the study of fixed points of nonlinear operators becomes more and more important.In this thesis,we mainly use the semi-order method to obtain some new fixed point theorems of decreasing operators and some theorems of set-valued decreasing operators under the condition that operators are not compact.The whole thesis is divided into three chapters.The first chapter is the introduction,which mainly introduces the development of fixed point problems in nonlinear functional,and lists some achievements of some scholars in this field.The second chapter introduces some basic concepts and results.In the third chapter,we study the fixed point theorems of decreasing operators,and use iterative technique to study some fixed point theorems of decreasing operators under noncompact and discontinuous conditions.In chapter 4,we study the fixed point theorems of set-valued strongly decreasing operators and set-valued totally decreasing operators without continuity and compactness,and obtain some new theorems.