On the Normality, Regularity and Chain-completeness of Partially Ordered Banach Spaces and Applications

TL;DR

This paper explores the properties of partially ordered Banach spaces, establishes fixed point theorems based on these properties, and applies them to prove the existence of solutions for certain integral equations.

Contribution

It introduces new fixed point theorems in partially ordered Banach spaces and applies them to solve integral equations, linking space properties with solution existence.

Findings

Fixed point theorems for partially ordered Banach spaces

Existence of solutions for Hammerstein integral equations

Connections between normality, regularity, and chain-completeness

Abstract

In this paper, we study the connections between the normality, regularity, full regularity, and chain-complete property in partially ordered Banach spaces. Then, by applying these properties, we prove some fixed point theorems on partially ordered Banach spaces. As applications of these fixed point theorems, we prove the existence of solutions of some integral equations, such as Hammerstein integral equations, in Banach spaces.