$\eta$-metric structures

TL;DR

This paper introduces $\\eta$-cone metric spaces, a new generalization of cone and metric type spaces, and establishes fixed point theorems within this framework, expanding the theoretical landscape of generalized metric spaces.

Contribution

The paper defines $\\eta$-cone metric spaces, explores their topological properties, and proves fixed point theorems, providing a novel extension of existing generalized metric space concepts.

Findings

$\\eta$-cone metric spaces generalize cone and metric type spaces.

Fixed point theorems are established for contractive maps in these spaces.

The new spaces exhibit natural topological properties.

Abstract

In this paper, we discuss recent results about generalized metric spaces and fixed point theory. We introduce the notion of $\eta$-cone metric spaces, give some topological properties and prove some fixed point theorems for contractive type maps on these spaces. In particular we show that theses $\eta$-cone metric spaces are natural generalizations of both cone metric spaces and metric type spaces.