Relations Between partial Metric Spaces and M-Metric Spaces, Caristi Kirk's Theorem in \(M-\)Metric Type Spaces

Very recently, Mehadi et al [M. Asadi, E. Karapınar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on \(M-\)metric spaces] extended the partial metric spaces to the notion of \(M-\)metric spaces. In this article, we study some relations between partial metric sp...

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Bibliographic Details
Published in:arXiv.org 2015-12
Main Authors: Abodayeh, K, Mlaiki, N, Abdeljawad, T, Shatanawi, W
Format: Article
Language:English
Subjects:
Fixed points (mathematics)
Theorems
Online Access:Get full text
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Summary:Very recently, Mehadi et al [M. Asadi, E. Karapınar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on \(M-\)metric spaces] extended the partial metric spaces to the notion of \(M-\)metric spaces. In this article, we study some relations between partial metric spaces and \(M-\)metric spaces. Also, we generalize Caristi Kirki's Theorem from partial metric spaces to \(M-\)metric spaces, where we corrected some gaps in the proof of the main Theorem in E. Karap\i nar [E. Karap\i nar, Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011: 4, (2011)]. We close our contribution by introducing some examples to validate and verify our extension results.
ISSN:2331-8422