Weak partial b-metric spaces and Nadler's theorem

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Kanwal T., Hussain A., Kumam P., SAVAŞ E.

Mathematics, vol.7, no.4, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.3390/math7040332
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Hausdorff metric space, Multivalued mappings, Nadler's theorem
  • Uşak University Affiliated: Yes

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.