Fixed Point Results for Dualistic Contractions with an Application. (22nd January 2020)

• Record Type: Journal Article
• Authors: Nazam, Muhammad; Mukheimer, Aiman; Aydi, Hassen; Arshad, Muhammad; Riaz, Raheel
• Other Names: Zhou Yong Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2020(2020)
• Publication Date: 2020-01-22
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2020/6428671
• Languages: English
• ISSNs: 1026-0226

Abstract

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.