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Mathematics 2019, 7(2), 132; https://doi.org/10.3390/math7020132

Fixed Point Results for Multi-Valued Contractions in b−Metric Spaces and an Application

1
Department of Mathematics, Faculty of Science and Technology, University Kebangsaan Malaysia, UKM Bangi, Selangor DE 43600, Malaysia
2
Department of Mathematics and General Courses, Prince Sultan University, Riyadh 11586, Saudi Arabia
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematics, College of Education in Jubail, Imam Abdulrahman Bin Faisal University, P.O. Box 12020, Industrial Jubail 31961, Saudi Arabia
*
Author to whom correspondence should be addressed.
These authors contributed equipollently to this work.
Received: 6 December 2018 / Revised: 12 January 2019 / Accepted: 16 January 2019 / Published: 1 February 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
Full-Text   |   PDF [772 KB, uploaded 1 February 2019]

Abstract

In this paper, by characterizing a weak contractive condition based on using C functions and α admissible multi-valued mapping of type S, we present some fixed point results for ( α , F ) admissible multi-valued mappings in the setting of b metric spaces. Some examples and an application are added in order to show the reliability of our obtained results. Our results amend, unify, and generalize some existing results in the literature. The scientific novelty of our main results is to take new contraction self-mappings in b metric spaces for multi-valued mappings. View Full-Text
Keywords: α−admissible mapping of type S; multi-valued mapping; Fixed point; b−metric space; Hausdorff metric α−admissible mapping of type S; multi-valued mapping; Fixed point; b−metric space; Hausdorff metric
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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Qawaqneh, H.; Md Noorani, M.S.; Shatanawi, W.; Aydi, H.; Alsamir, H. Fixed Point Results for Multi-Valued Contractions in b−Metric Spaces and an Application. Mathematics 2019, 7, 132.

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