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

• Autores: Md Ahmadullah, Mohammad Imdad, Mohammad Arif
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 19, Nº. 1, 2018, págs. 65-84
• Idioma: inglés
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• Resumen

  • 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.