Further extension of Nadler's fixed point theorem

TL;DR

This paper extends Nadler's fixed point theorem by generalizing Geraghty's theorem to multi-valued mappings, broadening the scope of fixed point results in mathematical analysis.

Contribution

It introduces a new generalized fixed point theorem for multi-valued mappings, expanding the applicability of existing fixed point principles.

Findings

Proves a generalized fixed point theorem for multi-valued mappings.

Extends Nadler's and Geraghty's fixed point theorems.

Provides theoretical foundations for further research in fixed point theory.

Abstract

In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.