Relation-theoretic metrical fixed point theorems under nonlinear contractions


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	Relation-theoretic metrical fixed point theorems under nonlinear contractions


	Fixed Point Theory, Volume 20, No. 1, 2019, 3-18, February 1st, 2019 DOI: 10.24193/fpt-ro.2019.1.01 Authors: Md Ahmadullah, Mohammad Imdad and Rqeeb Gubran Abstract: We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those contained in Samet and Turinici [Commun. Math. Anal. 13, 82-97 (2012)] and Alam and Imdad [J. Fixed Point Theory Appl. 17(4), 693-702 (2015)]. Interestingly a corollary to one of our main results proved under symmetric closure of any binary relation remains a sharpened version of a theorem due to Samet and Turinici. Finally, we use examples to highlight the realized improvements in the results proved in this paper. Key Words and Phrases: Complete metric spaces, binary relations, contraction mappings, fixed point. 2010 Mathematics Subject Classification: 47H10, 54H25. Published on-line: February 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents