%0 Journal Article
%T A Generalization of Preˋiˋ Type Mappings in 0-Complete Ordered Partial Metric Spaces
%A Satish Shukla
%A Stojan Radenoviˋ
%J Chinese Journal of Mathematics
%D 2013
%R 10.1155/2013/859531
%X The purpose of this paper is to prove some coincidence and common fixed point results for mappings satisfying Preˋiˋ type contraction condition in 0-complete ordered partial metric spaces. The results proved in this paper generalize and extend the results of Preˋiˋ and Matthews in 0-complete ordered partial metric spaces. Some examples are included which show that the generalization is proper. 1. Introduction Banach contraction mapping principle is one of the most interesting and useful tools in applied mathematics. In recent years many generalizations of Banach contraction mapping principle have appeared. In 1965 Preˋiˋ [1, 2] extended Banach contraction mapping principle to mappings defined on product spaces and proved the following theorem. Theorem 1. Let be a complete metric space, a positive integer, and a mapping satisfying the following contractive type condition: for every , where are nonnegative constants such that . Then there exists a unique point such that . Moreover if are arbitrary points in and for , then the sequence is convergent and . Note that condition (1) in the case reduces to the well-known Banach contraction mapping principle. So, Theorem 1 is a generalization of the Banach fixed point theorem. Some generalization of Theorem 1 can be seen in [1每11]. On the other hand in 1994 Matthews [12] introduced the notion of a partial metric space as a part of the study of denotational semantics of dataflow networks, showing that the Banach contraction mapping theorem can be generalized to the partial metric context for applications in program verification. In partial metric space the usual metric was replaced by partial metric, with a property that the self-distance of any point may not be zero. Result of Matthews is generalized by several authors in different directions (see, e.g., [13每29]). Romaguera [30] introduced the notion of -Cauchy sequence and -complete partial metric spaces and proved some characterizations of partial metric spaces in terms of completeness and -completeness. Some results on -complete partial metric spaces can be seen in [30每32]. The existence of fixed point in partially ordered sets was investigated by Ran and Reurings [33] and then by Nieto and Rodr赤guez-L車pez [34, 35]. Fixed point results in ordered partial metric spaces were obtained by several authors (see, e.g., [14, 16每19, 27, 29]). Very recently, in [7] (see also [36]) authors introduced the ordered Preˋiˋ type contraction and generalized the result of Preˋiˋ and proved some fixed point theorems for such mappings. In this paper, we generalize and extend the
%U http://www.hindawi.com/journals/cjm/2013/859531/