Existence of a solution to the satellite web coupling problem and generating neutrosophic fractals via a novel contraction

Muhammad Shaheryar; Fahim Ud Din; Luminiţa-Ioana Cotîrlă; Daniel Breaz; Muhammad Shaheryar; Fahim Ud Din; Luminiţa-Ioana Cotîrlă; Daniel Breaz

doi:10.3934/math.20251059

AIMS Mathematics

2025, Volume 10, Issue 10: 23821-23848. doi: 10.3934/math.20251059

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Existence of a solution to the satellite web coupling problem and generating neutrosophic fractals via a novel contraction

1.
Abdus Salam School of Mathematical Sciences, GCU, Lahore 54600, Pakistan
2.
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
3.
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
4.
Department of Mathematics, "1 Decembrie 1918" University of Alba Iulia, Alba Iulia 510009, Romania

Received: 28 March 2025 Revised: 25 June 2025 Accepted: 03 July 2025 Published: 21 October 2025
MSC : 54H25, 47H10

In this paper, we provide the notion of a generalized neutrosophic contraction, which extends the concepts of neutrosophic non-expansive mappings and neutrosophic Banach contractions. Using this approach, we proved a fixed point theorem and demonstrated the existence and uniqueness of a solution in the context of neutrosophic metric space and discussed its importance with some appealing applications such as the satellite web coupling problem. We also investigated a new avenue in fractal function production, where fractal structures are constructed using neutrosophic Hutchinson-Barnsley (NHB) operators. We have provided a variety of very interesting examples to illustrate the efficiency of our work in complicated dynamical systems, fractal geometry, and iterated function systems (IFS). We set the stage for future studies in applied mathematics, stability analysis, and fixed point theory by utilizing neutrosophic contraction principles.
- fixed point approximation,
- generalized neutrosophic iterated function system,
- satellite web coupling problem,
- generalized neutrosophic contraction,
- attractor,
- fractals
Citation: Muhammad Shaheryar, Fahim Ud Din, Luminiţa-Ioana Cotîrlă, Daniel Breaz. Existence of a solution to the satellite web coupling problem and generating neutrosophic fractals via a novel contraction[J]. AIMS Mathematics, 2025, 10(10): 23821-23848. doi: 10.3934/math.20251059

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Abstract

In this paper, we provide the notion of a generalized neutrosophic contraction, which extends the concepts of neutrosophic non-expansive mappings and neutrosophic Banach contractions. Using this approach, we proved a fixed point theorem and demonstrated the existence and uniqueness of a solution in the context of neutrosophic metric space and discussed its importance with some appealing applications such as the satellite web coupling problem. We also investigated a new avenue in fractal function production, where fractal structures are constructed using neutrosophic Hutchinson-Barnsley (NHB) operators. We have provided a variety of very interesting examples to illustrate the efficiency of our work in complicated dynamical systems, fractal geometry, and iterated function systems (IFS). We set the stage for future studies in applied mathematics, stability analysis, and fixed point theory by utilizing neutrosophic contraction principles.

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