Fixed point results for generalized cyclic contraction mappings in partial metric spaces
By Mujahid Abbas, Talat Nazir, Salvador Romaguera. RACSAM, 2011
70 citations recorded by the source corpus.
Rus (Approx. Convexity 3:171–178, 2005) introduced the concept of cyclic contraction mapping. Păcurar and Rus (Nonlinear Anal. 72:1181–1187, 2010) proved some fixed point results for cyclic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi }$$\end{document}-contraction mappings on a metric space. Karapinar (Appl. Math. Lett. 24:822–825, 2011) obtained a unique fixed point of cyclic weak \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi }$$\end{document}- contraction mappings and studied well-posedness problem for such mappings. On the other hand, Matthews (Ann. New York Acad. Sci. 728:183–197, 1994) introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In this paper, we initiate the study of fixed points of generalized cyclic contraction in the framework of partial metric spaces. We also present some examples to validate our results.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/5fd3e24fa154657a9163069f9b76efbc80101c4b
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In Geometry and Topology
- Hassen Aydi
- Calogero Vetro
- Mujahid Abbas
- Stojan Radenovic
- E. Karapınar
- Zoran Kadelburg
- Wasfi A. Shatanawi
- Bessem Samet
Citations in the corpus
- Common fixed points for multivalued generalized contractions on partial metric spaces (2014, methodology): “Confirming the interest for partial metric spaces [1,23], in this paper we extend the result of Wong to the case of two multivalued mappings that satisfy a generalized contractive condition in the framework of partial Hausdorff metric spaces.”