On fixed points of mappings with contractive iterates and iterative Ulam–Hyers stability in strong $ b $-metric spaces

Thanaa A. Alarfaj; Saud M. Alsulami; Thanaa A. Alarfaj; Saud M. Alsulami

doi:10.3934/math.2026935

AIMS Mathematics

2026, Volume 11, Issue 7: 23199-23209. doi: 10.3934/math.2026935

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On fixed points of mappings with contractive iterates and iterative Ulam–Hyers stability in strong $ b $-metric spaces

Thanaa A. Alarfaj ^{1
,
,},
Saud M. Alsulami ²

1.
Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31441, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 25 April 2026 Revised: 18 July 2026 Accepted: 21 July 2026 Published: 30 July 2026
MSC : 47A45, 47H09, 47H10

In this paper, we study a class of self-mappings that are not necessarily contractions but admit a contractive iterate at a point. Working in the framework of strong $ b $-metric spaces, we establish existence and uniqueness results for fixed points of such mappings. Moreover, we obtain an upper bound for the distance between an arbitrary initial point and the corresponding fixed point. Additionally, we investigate the behavior of fixed points under perturbations of the operator and prove the iterative Ulam–Hyers stability result for the associated fixed point problem.
- strong $ b $-metric space,
- mappings with contractive iteration at a point,
- iterative Ulam-Hyers stable
Citation: Thanaa A. Alarfaj, Saud M. Alsulami. On fixed points of mappings with contractive iterates and iterative Ulam–Hyers stability in strong $ b $-metric spaces[J]. AIMS Mathematics, 2026, 11(7): 23199-23209. doi: 10.3934/math.2026935

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Abstract

In this paper, we study a class of self-mappings that are not necessarily contractions but admit a contractive iterate at a point. Working in the framework of strong $ b $-metric spaces, we establish existence and uniqueness results for fixed points of such mappings. Moreover, we obtain an upper bound for the distance between an arbitrary initial point and the corresponding fixed point. Additionally, we investigate the behavior of fixed points under perturbations of the operator and prove the iterative Ulam–Hyers stability result for the associated fixed point problem.

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