Nonlinear contractions in metric spaces under locally $T$-transitive binary relations

By Aftab Alam, Mohammad Imdad. 2015

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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.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4f98c90fbcc4ba01e7023c83a5845f946b13db6e