  In this article, we generalize some frequently used metrical notions such as:
completeness, closedness, continuity, g-continuity and compatibility to
relation-theoretic setting and utilize these relatively weaker notions to prove
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 (Bull. Acad. Pol. Sci. Ser. Sci.
Math. Astron. Phys. 16 (1968) 733-735) and Jungck (Int. J. Math. Math. Sci. 9
(4) (1986) 771-779). In process our results generalize, extend, modify and
unify several well-known results especially those obtained in Alam and Imdad
(J. Fixed Point Theory Appl. 17 (4) (2015) 693-702), Karapinar et al: (Fixed
Point Theory Appl. 2014:92 (2014) 16 pp), Alam et al: (Fixed Point Theory Appl.
2014:216 (2014) 30 pp), Alam and Imdad (Fixed Point Theory, in press) and
Berzig (J. Fixed Point Theory Appl. 12 (1-2) (2012) 221-238.
