Fixed points and lines in 2-metric spaces

TL;DR

This paper explores special properties of bounded 2-metric spaces with an extra axiom, demonstrating that contractive mappings within these spaces have either a fixed point or a fixed line, expanding fixed point theory.

Contribution

It introduces a new class of bounded 2-metric spaces with an additional axiom and establishes the existence of fixed points or lines for contractive mappings in these spaces.

Findings

Contractive mappings have fixed points or fixed lines in the studied spaces

The paper defines a new class of 2-metric spaces with an extra axiom

Fixed point or line existence is guaranteed under these conditions

Abstract

We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.