On Fixed Point Theorems of Mixed Monotone Operators

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 for sums of operators

Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces

There are a lot of fixed and common fixed point results in different types of spaces. For example, metric spaces, fuzzy metric spaces, and uniform spaces. One of the most interesting is partial metric space, which is defined by Matthews 1 . In partial metric spaces, the distance of a point in the self may not be zero. After the definition of partial metric space, Matthews proved the partial met...

On a fixed point theorem of mixed monotone operators and applications

In this paper, by introducing τ −φ− mixed monotone operators in ordered Banach spaces, the existence and uniqueness theorems for the operators are obtained. In the end, the new results are used to study the existence of positive solutions to second order equations with Neumann boundary conditions.