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Weak Partial b -Metric Spaces and Nadler’s Theorem

Author

Listed:
  • 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
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Ekrem Savas

    (Department of Mathematics, Usak University, Usak 64000, Turkey)

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.

Suggested Citation

  • Tanzeela Kanwal & Azhar Hussain & Poom Kumam & Ekrem Savas, 2019. "Weak Partial b -Metric Spaces and Nadler’s Theorem," Mathematics, MDPI, vol. 7(4), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:332-:d:220298
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