Nonlinear contractions in metric spaces under locally T-transitive binary relations
General Topology
2016-03-03 v4 Functional Analysis
Abstract
In this paper, we present a variant of Boyd-Wong fixed point theorem in a metric space equipped with a locally T-transitive binary relation, which under universal relation reduces to Boyd-Wong (Proc. Amer. Math. Soc. 20 (1969) 458-464) and Jotic (Indian J. Pure Appl. Math. 26 (1995) 947-952) fixed point theorems. Also, our results extend several other well-known fixed point theorems such as: Alam and Imdad (J. Fixed Point Theory Appl. 17 (4) (2015) 693-702) and Karapinar and Roldan-Lopez-de-Hierro (J. Inequal. Appl. 2014:522 (2014) 12 pp) besides some others.
Cite
@article{arxiv.1512.00348,
title = {Nonlinear contractions in metric spaces under locally T-transitive binary relations},
author = {Aftab Alam and Mohammad Imdad},
journal= {arXiv preprint arXiv:1512.00348},
year = {2016}
}