Banach and Suzuki-type fixed point theorems in Generalized $n$-metric spaces with an application

TL;DR

This paper extends fixed point theorems to Generalized n-metric spaces, broadening the scope of Banach and Suzuki-type results with applications to functional equations in dynamic programming.

Contribution

It introduces fixed point theorems in Generalized n-metric spaces, generalizing previous metric space results and applying them to functional equations.

Findings

Proved Banach fixed point theorem in Generalized n-metric spaces

Established Suzuki-type fixed point theorem in these spaces

Applied fixed point results to functional equations in dynamic programming

Abstract

Mustafa and Sims [12] introduced the notion of $G$-metric as a possible generalization of usual notion of a metric space. The author generalized the notion of G-metric to more than three variables and introduced the concept of Generalized $n$-metric spaces [10]. In this paper, We prove Banach fixed point theorem and a Suzuki-type fixed point theorem in Generalized $n$-metric spaces. We also discuss applications to certain functional equations arising in dynamic programming.