Fixed point theorems for enriched Kannan-type mappings and application

Yao Yu; Chaobo Li; Dong Ji; Yao Yu; Chaobo Li; Dong Ji

doi:10.3934/math.20241048

AIMS Mathematics

2024, Volume 9, Issue 8: 21580-21595. doi: 10.3934/math.20241048

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Fixed point theorems for enriched Kannan-type mappings and application

Yao Yu ¹,
Chaobo Li ^{2
,
,},
Dong Ji ^1,2

1.
Department of Mathematics, Harbin University, Harbin 150086, China
2.
Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Received: 06 May 2024 Revised: 25 June 2024 Accepted: 01 July 2024 Published: 05 July 2024
MSC : 47H10, 54H25

The aim of this paper is to establish some fixed point results for enriched Kannan-type mappings in convex metric spaces. We first give an affirmative answer to a recent Berinde and Păcurar's question (Remark 2.3) [J. Comput. Appl. Math., 386 (2021), 113217]. Furthermore, we establish the existence and uniqueness of fixed points for Suzuki-enriched Kannan-type mappings in the setting of convex metric spaces. Finally, we present an application to approximate the solution of the Volterra integral equations to support our results.
- fixed point,
- enriched Kannan mapping,
- suzuki mapping,
- convex metric space
Citation: Yao Yu, Chaobo Li, Dong Ji. Fixed point theorems for enriched Kannan-type mappings and application[J]. AIMS Mathematics, 2024, 9(8): 21580-21595. doi: 10.3934/math.20241048

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Abstract

The aim of this paper is to establish some fixed point results for enriched Kannan-type mappings in convex metric spaces. We first give an affirmative answer to a recent Berinde and Păcurar's question (Remark 2.3) [J. Comput. Appl. Math., 386 (2021), 113217]. Furthermore, we establish the existence and uniqueness of fixed points for Suzuki-enriched Kannan-type mappings in the setting of convex metric spaces. Finally, we present an application to approximate the solution of the Volterra integral equations to support our results.

References

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