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Research Article | Open Access

Answers to questions on Kannan's fixed point theorem in strong b-metric spaces

Peng Wang, Fei He( ), Xuan Liu
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
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Abstract

Our purpose of this paper is to answer several open questions posed by Doan (AIMS Math., 6 (2021), 7895–7908). First, we present two fixed point theorems, which are positive answers to Doan's questions. Second, we establish a new type of Riech's fixed point theorem to improve a result of Doan. Finally, we offer a straightforward example illustrating that a set-valued mapping satisfying the conditions of our fixed point theorem may has more than one fixed point.

Keywords

fixed pointstrong b-metric spaceGeraghty functionsKannan mappingRiech's fixed point theoremmulti-valued mapping
CLC number: 47H10, 54H25

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 3671-3684
DOI: 10.3934/math.2024180

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Cite this article:
Wang P, He F, Liu X. Answers to questions on Kannan's fixed point theorem in strong b-metric spaces. AIMS Mathematics, 2024, 9(2): 3671-3684. https://doi.org/10.3934/math.2024180

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Received: 10 November 2023
Revised: 21 December 2023
Accepted: 26 December 2023
Published: 15 February 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)