Double controlled cone metric spaces and the related fixed point theorems

TL;DR

This paper introduces double controlled cone metric spaces using two control functions, provides examples distinguishing them from controlled metric spaces, and establishes fixed point theorems for contractions within this new framework.

Contribution

It defines a novel class of double controlled cone metric spaces and proves fixed point theorems for Banach and Kannan contractions in this setting.

Findings

Example of a double controlled cone metric space not being a controlled metric space

Fixed point theorems for Banach type contractions

Fixed point theorems for Kannan type contractions

Abstract

In this paper, we introduce double controlled cone metric spaces via two control functions. An example of a double controlled cone metric space by two incomparable functions, which is not a controlled metric space, is given. We also provide some fixed point results involving Banach type and Kannan type contractions in the setting of double controlled cone metric spaces.