Common fixed points of mappings satisfying implicit relations in partial metric spaces

Abstract

, introduced and studied the concept of partial metric space, as a part of the study of denotational semantics of dataflow networks. He also obtained a Banach type fixed point theorem on complete partial metric spaces. Very recently Berinde and Vetro, [V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory and Applications 2012, 2012:105], discussed, in the setting of metric and ordered metric spaces, coincidence point and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation. In this work, in the setting of partial metric spaces, we study coincidence point and common fixed point theorems for two self-mappings satisfying generalized contractive conditions, defined by implicit relations. Our results unify, extend and generalize some related common fixed point theorems of the literature.

Unique common fixed point theorems on partial metric spaces

“…The common fixed point theorems for mappings satisfying certain contractive conditions in metric spaces have been continually studied for decade (see [1,3,5,6,8,9,10,11,12,14,15] and references contained therein). In 1976, Jungck [7] proved the existence of common fixed point theorems for commuting mappings in metric spaces where the results require the continuity of one of two such mappings.…”

A general fixed point theorem for a pair of multi-valued mappings in partial metric spaces

“…Also, the method allows the study of local and global properties of fixed point structures. The study of fixed points for self mappings in complete partial metric spaces satisfying an implicit relation is initiated in [17].…”

Some results of common fixed point for four self-maps satisfying a new Ψ -contractive condition in partial metric spaces

“…In [20], Matthews extended the well known Banach contraction principle from metric spaces to partial metric spaces. Later in [1]- [19] and [21]- [28], several authors obtained some fixed point results for mappings satisfying different contractive conditions.…”