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Relation-theoretic metrical coincidence theorems

Alam Aftab (Department of Mathematics, Aligarh Muslim University, AMU, Aligarh, UP, India)
Imdad Mohammad (Department of Mathematics, Aligarh Muslim University, AMU, Aligarh, UP, India)

In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, 1-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove our results on the existence and uniqueness of coincidence points involving a pair of mappings defined on a metric space endowed with an arbitrary binary relation. Particularly, under universal relation our results deduce the classical coincidence point theorems of Goebel, Jungck and others. Furthermore, our results generalize, modify, unify and extend several well-known results of the existing literature.

Keywords: Binary relations, R-completeness, R-continuity, R-connected sets, d-self-closedness