Weak Partial b -Metric Spaces and Nadler’s Theorem

Tanzeela Kanwal, Azhar Hussain, Poom Kumam and Ekrem Savas
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Tanzeela Kanwal: Govt. Degree College for Women Malakwal, Malakwal, Mandi Bahuaddin 50400, Pakistan
Azhar Hussain: Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan
Poom Kumam: 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
Ekrem Savas: Department of Mathematics, Usak University, Usak 64000, Turkey

Mathematics, 2019, vol. 7, issue 4, 1-12

Abstract: 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.

Keywords: multivalued mappings; Hausdorff metric space; Nadler’s theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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