On multidimensional fixed-point theorems and their applications

TL;DR

This paper introduces new multidimensional fixed-point theorems and demonstrates their application in proving the existence and uniqueness of solutions to nonlinear integral equations, supported by illustrative examples.

Contribution

It presents a novel multidimensional fixed-point theorem and applies it to solve nonlinear Hammerstein integral equations, expanding fixed-point theory applications.

Findings

Established a new multidimensional fixed-point theorem.

Proved existence and uniqueness of solutions for a class of nonlinear integral equations.

Provided an example illustrating the theoretical results.

Abstract

The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a solution of a nonlinear Hammerstein integral equation. Moreover, we provide an example to illustrate the hypotheses and the abstract result of this paper.