New fixed point theorems and applications of mixed monotone operator

On Fixed Point Theorems of Mixed Monotone Operators

Mixed monotone operators were introduced by Guo and Lakshmikantham in 1 in 1987. Thereafter many authors have investigated these kinds of operators in Banach spaces and obtained a lot of interesting and important results. They are used extensively in nonlinear differential and integral equations. In this paper, we obtain some new existence and uniqueness theorems of positive fixed point of mixe...

Fixed Point Theorems of a Class of Mixed Monotone Operators and Applications

Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In the paper, without any compact or continuous assumptions, we study the uniqueness and existence of fixed points of mixed monotone operators in a partially ordered Banach space. Our conclusions extend and improve previous results. As...

Fixed Point Theorems and Applications

New Best Proximity Point Theorems with Applications to Simultaneous Generalizations of Common Fixed Point Theorems

In this work, we first introduce the concept of approximate sequence and establish some new convergence theorems for approximate sequences. By applying our new convergence theorems, we obtain new best proximity point theorems which improve and generalize some known results in the literature. As applications, some simultaneous generalizations of common fixed point theorems of Banach type, Kannan...

Krasnoselskii Type Fixed Point Theorems and Applications

In this paper, we establish two fixed point theorems of Krasnoselskii type for the sum of A + B, where A is a compact operator and I − B may not be injective. Our results extend previous ones. As an application, we apply such results to obtain some existence results of periodic solutions for delay integral equations and then give three instructive examples.