Partial Metric Spaces

Common fixed point results of four mappings in ordered partial metric spaces

“…Karapinar [25] proved some fixed point theorems for weak φ− contraction on partial metric spaces in partially ordered sets. Further results in the direction of partial metric space were proved in [1,3,5,10,14,15,44,48].…”

“…For some more examples of partial metric spaces, we refer to [1,3,7,15,43,46]. Each partial metric p on X generates a T 0 topology τp on X which has as a base the family open p-balls {Bp(x, ε) : x ∈ X, ε > 0}, where Bp(x, ε) = {y ∈ X : p(x, y) < p(x, x) + ε}, for all x ∈ X and ε > 0.…”

Common fixed points of generalized rational contractions on a closed ball in partial metric spaces

“…Consistent with [8,9,[12][13][14][15][16], the following definitions and results will be needed in the sequel. Throughout this paper, we denote (0, ∞) by R + , [0, ∞) by R + 0 , (−∞, +∞) by R and set of natural numbers by N.…”

Coincidence Theorems for Comparable Generalized Non Linear Contractions in Ordered Partial Metric Spaces

“…Matthews [16] extended the Banach contraction mapping theorem to the partial matric spaces for applications in program verification. Subsequently several authors (see for instance, [7,9,21,24,32]) obtained many useful fixed point results in this direction. The existence of several connection between partial metrics and topological aspects of domain theory has been pointed by many authors see [9,10,15,16,25,26,27].…”