Exploring new geometric contraction mappings and their applications in fractional metric spaces

Haitham Qawaqneh; Hasanen A. Hammad; Hassen Aydi; Haitham Qawaqneh; Hasanen A. Hammad; Hassen Aydi

doi:10.3934/math.2024028

AIMS Mathematics

2024, Volume 9, Issue 1: 521-541. doi: 10.3934/math.2024028

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Research article

Exploring new geometric contraction mappings and their applications in fractional metric spaces

1.
Department of Mathematics, Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
2.
Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
4.
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
5.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
6.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 14 September 2023 Revised: 10 November 2023 Accepted: 20 November 2023 Published: 30 November 2023
MSC : 34B15, 47H10, 54H25

This article delves deeply into some mathematical basic theorems and their diverse applications in a variety of domains. The major issue of interest is the Banach Fixed Point Theorem (BFPT), which states the existence of a unique fixed point in fractional metric spaces. The significance of this theorem stems from its utility in a variety of mathematical situations for approximating solutions and resolving iterative problems. On this foundational basis, the study expands by introducing the concept of fractional geometric contraction mappings, which provide a new perspective on how convergence develops in fractional metric spaces.
- fractional metric space,
- geometric contraction mappings,
- convergence,
- fractional derivatives
Citation: Haitham Qawaqneh, Hasanen A. Hammad, Hassen Aydi. Exploring new geometric contraction mappings and their applications in fractional metric spaces[J]. AIMS Mathematics, 2024, 9(1): 521-541. doi: 10.3934/math.2024028

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Abstract

This article delves deeply into some mathematical basic theorems and their diverse applications in a variety of domains. The major issue of interest is the Banach Fixed Point Theorem (BFPT), which states the existence of a unique fixed point in fractional metric spaces. The significance of this theorem stems from its utility in a variety of mathematical situations for approximating solutions and resolving iterative problems. On this foundational basis, the study expands by introducing the concept of fractional geometric contraction mappings, which provide a new perspective on how convergence develops in fractional metric spaces.

References

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