Common fixed points for a pair of commuting mappings in complete cone metric spaces

TL;DR

This paper extends fixed point theorems for commuting mappings in complete cone metric spaces by introducing generalized contraction notions and proving their fixed point results.

Contribution

It introduces generalized contraction concepts like Kannan, Zamfirescu, and Weak Contraction in cone metric spaces and proves their fixed point theorems.

Findings

Proved fixed point theorems for generalized contractions in cone metric spaces.

Extended Singh's fixed point theorem to broader classes of mappings.

Established new conditions for the existence of common fixed points.

Abstract

This paper is devoted to prove the S. L. Singh's common fixed point Theorem for commuting mappings in cone metric spaces. In this framework, we introduce the notions of Generalized Kannan Con- traction, Generalized Zamfirescu Contraction and Generalized Weak Contraction for a pair of mappings, proving afterward their respective fixed point results.