Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application

Abstract

. In this paper, we prove fixed point theorem for weakly contractive mappings using locally T -transitivity of binary relation and presenting an analogous ver-sion of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions. Our fixed point results under universal relation reduces to Harjani and Sadarangani [Nonlinear Anal., 71 (2009), 3403–3410] fixed point theorems. In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.