Strong tripled fixed points under a new class of F-contractive mappings with supportive applications

Hasanen A. Hammad; Doha A. Kattan; Hasanen A. Hammad; Doha A. Kattan

doi:10.3934/math.2025266

AIMS Mathematics

2025, Volume 10, Issue 3: 5785-5805. doi: 10.3934/math.2025266

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Research article

Strong tripled fixed points under a new class of F-contractive mappings with supportive applications

Hasanen A. Hammad ^{1,2
,
,},
Doha A. Kattan ³

1.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
3.
Department of Mathematics, College of Sciences and Art, King Abdulaziz University, Rabigh, Saudi Arabia

Received: 27 December 2024 Revised: 27 February 2025 Accepted: 04 March 2025 Published: 14 March 2025
MSC : 47H10, 47H09, 26A33, 54G05, 45G10

A significant advancement in the field of fixed point theory is presented in this manuscript. The existence and uniqueness of strong tripled coincidence points for F-contractive mappings in metric spaces were investigated. An extension of this analysis to multivalued F-contractive mappings was provided, establishing the existence of tripled fixed points within this generalized setting. Existing findings in the literature were generalized and refined by these results, offering a more comprehensive understanding of fixed point phenomena. Furthermore, the practical applicability of these theoretical contributions was demonstrated through the study of solutions to various forms of nonlinear integral equations and integral-type inequalities.
- tripled fixed point,
- nonlinear equation,
- F-contraction mapping,
- evaluation metrics,
- standard metric space
Citation: Hasanen A. Hammad, Doha A. Kattan. Strong tripled fixed points under a new class of F-contractive mappings with supportive applications[J]. AIMS Mathematics, 2025, 10(3): 5785-5805. doi: 10.3934/math.2025266

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Abstract

A significant advancement in the field of fixed point theory is presented in this manuscript. The existence and uniqueness of strong tripled coincidence points for F-contractive mappings in metric spaces were investigated. An extension of this analysis to multivalued F-contractive mappings was provided, establishing the existence of tripled fixed points within this generalized setting. Existing findings in the literature were generalized and refined by these results, offering a more comprehensive understanding of fixed point phenomena. Furthermore, the practical applicability of these theoretical contributions was demonstrated through the study of solutions to various forms of nonlinear integral equations and integral-type inequalities.

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