Infinite Geraghty type extensions and its applications on integral equations

TL;DR

This paper extends Geraghty type theorems to infinite dimensions, providing new solutions for infinite dimensional integral equations using advanced fixed point techniques.

Contribution

It introduces infinite dimensional extensions of Geraghty theorems and applies them to solve complex integral equations.

Findings

Extended Geraghty theorems to infinite dimensions.

Developed solutions for infinite dimensional Fredholm and Uryshon integral equations.

Provided theoretical framework for applications in integral equations.

Abstract

In this article, we go on to discuss about a series of infinite dimensional extension of the theorems in [3], [5], [6]. We also prove a similar Geraghty type constructions for Fisher ([5]) in infinite dimension, using similar techniques as in [3] and [6]. As an application a theory of finding solutions for the infinite dimensional Fredholm integral equation and Uryshon type integral equation is also provided.