Fixed Point Theorems And Generalizations On Mixed Monotone Operators

The purpose of this thesis is to study the problems of the existence and uniqueness of fixed points of mixed monotone operators, anti-mixed monotone operators, non-mixed monotone operators, non-antimixed monotone operators without continuity and compactness conditions in Banach spaces, by means of the cone and partial ordering method and non-symmetric iterative techniques. Finally, a kind of fixed point theorems for anti-mixed monotone operators are given, which can change the operator solution.This thesis contains four chapters.In chapter 1, we introduce the background and current situation about mixed monotone operators. Some elementary knowledge and concepts which will be used in this thesis are also given.In chapter 2, a mixed monotone operator theorem is improved and developed according to fixed point theorems on mixed monotone operators combining the initial conditions under which bound norn or sequential compression devices are discussed.In chapter 3, an anti-mixed monotone operator theorem is improved and developed according to fixed point theorems on anti-mixed monotone operators combining the initial conditions under which bound norn or sequential compression devices are discussed.In chapter 4, a fixed point theorem on non-mixed monotone operators, non-antimixed monotone operators, non-increasing (non-decreasing) operators as well as a kind of fixed point theorems on anti-mixed monotone operators which can change the operator solution are discussed.