Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions
General Mathematics
2017-05-09 v1
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.
Cite
@article{arxiv.1705.02886,
title = {Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions},
author = {Md Ahmadullah and Mohammad Imdad and Mohammad Arif},
journal= {arXiv preprint arXiv:1705.02886},
year = {2017}
}
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15 page