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Weak Partial b-Metric Spaces and Nadler’s Theorem

Govt. Degree College for Women Malakwal, Malakwal, Mandi Bahuaddin 50400, Pakistan
Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) and KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Department of Mathematics, Usak University, Usak 64000, Turkey
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 332;
Received: 4 March 2019 / Revised: 29 March 2019 / Accepted: 1 April 2019 / Published: 5 April 2019
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
PDF [366 KB, uploaded 5 April 2019]


The purpose of this paper is to define the notions of weak partial b-metric spaces and weak partial Hausdorff b-metric spaces along with the topology of weak partial b-metric space. Moreover, we present a generalization of Nadler’s theorem by using weak partial Hausdorff b-metric spaces in the context of a weak partial b-metric space. We present a non-trivial example which show the validity of our result and an application to nonlinear Volterra integral inclusion for the applicability purpose. View Full-Text
Keywords: multivalued mappings; Hausdorff metric space; Nadler’s theorem multivalued mappings; Hausdorff metric space; Nadler’s theorem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Kanwal, T.; Hussain, A.; Kumam, P.; Savas, E. Weak Partial b-Metric Spaces and Nadler’s Theorem. Mathematics 2019, 7, 332.

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