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Open AccessArticle

New Extensions of Kannan’s and Reich’s Fixed Point Theorems for Multivalued Maps Using Wardowski’s Technique with Application to Integral Equations

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Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam 788011, India
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Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
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Authors to whom correspondence should be addressed.
Symmetry 2020, 12(7), 1090; https://doi.org/10.3390/sym12071090 (registering DOI)
Received: 27 May 2020 / Revised: 8 June 2020 / Accepted: 19 June 2020 / Published: 1 July 2020
The metric function generalizes the concept of distance between two points and hence includes the symmetric property. The aim of this article is to introduce a new and proper extension of Kannan’s fixed point theorem to the case of multivalued maps using Wardowski’s F-contraction. We show that our result is applicable to a class of mappings where neither the multivalued version of Kannan’s theorem nor that of Wardowski’s can be applied to determine the existence of fixed points. Application of our result to the solution of integral equations has been provided. A multivalued Reich type generalized version of the result is also established. View Full-Text
Keywords: fixed point; multivalued map; F-contraction; complete metric space; integral equation fixed point; multivalued map; F-contraction; complete metric space; integral equation
MDPI and ACS Style

Debnath, P.; Srivastava, H.M. New Extensions of Kannan’s and Reich’s Fixed Point Theorems for Multivalued Maps Using Wardowski’s Technique with Application to Integral Equations. Symmetry 2020, 12, 1090.

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