Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions

Md Ahmadullah; Mohammad Imdad; Mohammad Arif

doi:10.4995/agt.2018.7677

Authors

Md Ahmadullah Aligarh Muslim University
Mohammad Imdad Aligarh Muslim University
Mohammad Arif Aligarh Muslim University

DOI:

https://doi.org/10.4995/agt.2018.7677

Keywords:

Complete metric spaces, binary relations, contraction mappings, fixed point

Abstract

In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))] and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper.

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Author Biographies

Md Ahmadullah, Aligarh Muslim University

Department of Mathematics

Mohammad Imdad, Aligarh Muslim University

Department of Mathematics

Mohammad Arif, Aligarh Muslim University

Department of Mathematics

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