A unified theory of cone metric spaces and its applications to the fixed point theory

TL;DR

This paper develops a unified theoretical framework for cone metric spaces over solid vector spaces and applies it to fundamental fixed point theorems like Banach's contraction principle.

Contribution

It introduces a comprehensive theory for cone metric spaces over solid vector spaces and extends key fixed point results within this framework.

Findings

Unified theory for cone metric spaces over solid vector spaces

Full statements of iterated contraction and Banach contraction principles in this context

Extension of classical fixed point theorems to cone metric spaces

Abstract

In this paper we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces over a solid vector space.