  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.
