Generalization And Application Of Some Fixed Point Theorems In Partially Ordered Spaces

In this thesis,combining with the mixed monotone operator,we first prove some new Krasnoselskii-type coupled fixed point theorems;By establishing a new contractive condition,we prove new coupled coincidence and coupled common fixed point,theorems;By using the measure of noncompactness,some new fixed point theorems and coupled fixed point theorems for condensing operators are obtained in partially ordered Banach spaces.Then.applying these new coupled fixed point the-orems to Caputo fractional differential systems and integral systems,the existence and uniqueness of solutions we proved.The main results of this paper are as follows:1.By combining the mixed monotone operator,some new Krasnoselskii-type coupled fixed point theorems are proved in partially ordered Banach spaces.Then apply the new coupled fixed point theorem to prove the existence of solutions for Caputo fractional systems.2.By weakening the contractive condition of the existing theorem,we establish a new contractive condition and prove the new coupled coincidence and coupled common fixed point theorems in partially ordered metric spaces.Then apply the new coupled common fixed point theorem to prove the existence and uniqueness of solutions for integral systems.3.By introducing two classes of functions R,(?),and using the measure of noncompactness,we obtain some new fixed point theorems and coupled fixed point theorems for condensing operators in partially ordered Banach spaces.Then apply these new coupled fixed point theorems to prove the existence of solutions for a class of integral systems.