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

Md Ahmadullah, Mohammad Imdad, Mohammad Arif


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.


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

Subject classification

47H10; 54H25

Full Text:



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