Comparable linear contractions in ordered metric spaces

TL;DR

This paper introduces g-comparability in ordered metric spaces to improve contraction theorems, extending classical results on coincidence points without requiring g-monotonicity.

Contribution

It proposes a new notion of g-comparability to generalize and strengthen existing fixed point theorems in ordered metric spaces.

Findings

Established existence and uniqueness of coincidence points under new conditions.

Extended classical fixed point results to broader settings.

Removed the need for g-monotonicity in contraction mappings.

Abstract

In this paper, with a view to improve the g-monotonicity condition, we introduce the notion of g-comparability of a mapping defined on an ordered set and utilize the same to prove some existence and uniqueness results on coincidence points for linear contraction without g-monotonicity in ordered metric spaces. Our results extend some classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. 132(2004), no.5, 1435-1443), Nieto and Rodriguez-Lopez (Acta Math. Sin. 23(2007), no.12, 2205-2212), Turinici (Libertas Math. 31(2011), 49-55), Turinici (Math. Student 81(2012), no.1-4, 219-229) and Doric et al. (RACSAM 108(2014), no.2, 503-510) and similar others.