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

Peng Wang; Fei He; Xuan Liu; Peng Wang; Fei He; Xuan Liu

doi:10.3934/math.2024180

AIMS Mathematics

2024, Volume 9, Issue 2: 3671-3684. doi: 10.3934/math.2024180

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Research article

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

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received: 10 November 2023 Revised: 21 December 2023 Accepted: 26 December 2023 Published: 09 January 2024
MSC : 47H10, 54H25

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.
- fixed point,
- strong $ b $-metric space,
- Geraghty functions,
- Kannan mapping,
- Riech's fixed point theorem,
- multi-valued mapping
Citation: Peng Wang, Fei He, Xuan Liu. Answers to questions on Kannan's fixed point theorem in strong $ b $-metric spaces[J]. AIMS Mathematics, 2024, 9(2): 3671-3684. doi: 10.3934/math.2024180

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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.

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