Relation-theoretic contraction principle in metric-like as well as   partial metric spaces
  In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are sharper versions of the corresponding known results of the existing literature. Finally, we use an example to demonstrate our main result. 
Md Ahmadullah, Abdur Rauf Khan, and Mohammad Imdad
math.GM