Several Fixed Point Theorems on Partially Ordered Banach Spaces and Applications

TL;DR

This paper establishes new fixed point theorems in partially ordered Banach spaces and applies them to prove existence and uniqueness of solutions for integral and equilibrium problems.

Contribution

It introduces several fixed point theorems based on properties like normality and regularity in partially ordered Banach spaces, with applications to integral and equilibrium problems.

Findings

Proved fixed point theorems in normal and regular partially ordered Banach spaces.

Established existence and uniqueness results for integral equations.

Demonstrated solvability of certain equilibrium problems.

Abstract

In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by applying these theorems, we provide some existence and uniqueness of solutions to some integral equations. We also prove the solvability of some equilibrium problems in Banach spaces.