A New Fixed Point Theorem Of Mixed Monotone Operator And Its Applications

In this paper, two kinds of mixed monotone operators are discussed, with the aidof iterative technique, new fixed point theorems are obtained. Finally, the new resultsare applied to the nonlinear integral equation and the nonlinear fractional differentialequation.The Paper consists of three chapters.In Chapter1, we introduce the backgrounds of our studies and main content of thispaper.In Chapter2, a class of mixed monotone operators with positive linear term isdiscussed. With the aid of iterative technique, a new fixed point theorem is obtained,and the results are applied to investigating the existence of positive almost periodicsolutions for a nonlinear integral equation.In Chapter3, we mainly study the existence and uniqueness of fixed point formixed monotone operators with sub-homogeneous. Some new results are obtained. Weapply the new results to a nonlinear integral equation. some existing are improved andgeneralized.