Existence and uniqueness of fixed point for ordered contraction type operator in Banach Space

TL;DR

This paper proves the existence and uniqueness of fixed points for certain contraction operators in Banach spaces, with applications to solving integral and differential equations.

Contribution

It establishes new fixed point theorems for ordered contraction operators in Banach spaces, extending previous results.

Findings

Fixed point existence under specific contraction conditions

Uniqueness of solutions for related equations

Applications to integral and differential equations

Abstract

In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.