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Nadler and Kannan Type Set Valued Mappings in M-Metric Spaces and an Application

1
Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India
2
Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
3
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat 395007, Gujarat, India
5
Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 373; https://doi.org/10.3390/math7040373
Received: 27 February 2019 / Revised: 16 April 2019 / Accepted: 18 April 2019 / Published: 24 April 2019
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
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PDF [263 KB, uploaded 24 April 2019]

Abstract

This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory. View Full-Text
Keywords: homotopy; M-metric; M-Pompeiu–Hausdorff type metric; multivalued mapping; fixed point homotopy; M-metric; M-Pompeiu–Hausdorff type metric; multivalued mapping; fixed point
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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MDPI and ACS Style

Patle, P.R.; Kumar Patel, D.; Aydi, H.; Gopal, D.; Mlaiki, N. Nadler and Kannan Type Set Valued Mappings in M-Metric Spaces and an Application. Mathematics 2019, 7, 373.

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