Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application (Analysis in Theory and Applications, 2022)
In this paper, we prove fixed point theorem for weakly contractive mappings using locally $T$-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoreticmetrical notions. Our fixed point results under universal relation reduces to Harjaniand Sadarangani [Nonlinear Anal., 71 (2009), 3403–3410] fixed point theorems. In thisway we also generalize some of the recent fixed point theorems for weak contractionin the existing literature.