Weak partial b-metric spaces and Nadler's theorem

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. © 2019 by the authors.Faculty of Science, Maejo University King Mongkut's University of Technology Thonburi Türkiye Bilimler AkademisiFunding: This project was supported by Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart Innovation research Cluster (CLASSIC), Faculty of Science, KMUTT.Acknowledgments: This project was completed during the visit of second author to Usak University, Turkey, sponsored by Turkish Academy of Sciences