Abstract
In this paper, by introducing a convergence comparison property of a self-mapping, we establish some new fixed point theorems for Bianchini type, Reich type, and Dass-Gupta type dualistic contractions defined on a dualistic partial metric space. Our work generalizes and extends some well known fixed point results in the literature. We also provide examples which show the usefulness of these dualistic contractions. As an application of our findings, we demonstrate the existence of the solution of an elliptic boundary value problem.
Highlights
Is Contraction principle has been studied in partial metric spaces (PMS) introduced by Matthews [18]. e PMS generalizes the metric space where the self-distance may be not equal to zero. e topological concepts, like convergence, Cauchy sequence, continuity, and completeness in this class can be found in [18,19,20,21] and references there in
O’Neill [22] initiated the notion of a dualistic partial metric space. is class generalizes the notion of partial metric spaces
O’Neill [22] studied various topological properties of a dualistic partial metric space, while xed point theory on dualistic partial metric spaces was presented by Oltra and Valero [23], who proved a Banach xed point theorem and gave convergence properties of sequences on complete dualistic partial metric spaces
Summary
We begin with the following useful property. Let be a self-mapping on a dualistic partial metric space A , ∗. If there is a convergent sequence in A with → , such that. Is said to have the convergence comparison property [in short, (CCP)]
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