TY - JOUR
T1 - Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application
AU - Prasad , Gopi
AU - Dimri , Ramesh Chandra
JO - Analysis in Theory and Applications
VL - 2
SP - 232
EP - 242
PY - 2022
DA - 2022/07
SN - 38
DO - http://doi.org/10.4208/ata.OA-2017-0044
UR - https://global-sci.org/intro/article_detail/ata/20800.html
KW - $\mathcal{R}$-continuity, locally $T$-transitive binary relation, weakly contractive map.
AB - <p style="text-align: justify;">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 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.</p>