Common fixed-point results for nonlinear contractions in ordered partial metric spaces

Abstract

In this paper, a new class of a pair of generalized nonlinear contractions on partially ordered partial metric spaces is introduced, and some coincidence and common fixed-point theorems for these contractions are proved. Presented theorems are twofold generalizations of very recent fixed-point theorems of Altun and Erduran (Fixed Point Theory

Generalized Geraghty type mappings on partial metric spaces and fixed point results

“…Also,Ćirić et al [8], Samet et al [21] and Shatanawi et al [22] proved some common fixed point results in partial metric spaces. The best two generalizations of it were given by Romaguera [19,20].…”

Suzuki type common fixed point theorem in complete metric space and partial metric space

“…[27] Let (X, p) be a partial metric space and F, : X → X are mappings of X into itself. We say that the pair {F, } is partial compatible if the following conditions hold:…”

“…The utility of compatibility in the context of fixed point theory was demonstrated by extending a theorem of Park-Bae [25]. Recently Samet et al [27] introduced a definition of compatible pair of mappings in partial metric spaces. In this paper we prove that two compatible mapping have unique common fixed point in metric and partial metric spaces respectively.…”

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

“…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].…”