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A new approach to fractals via best proximity point

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  • Altun, Ishak
  • Sahin, Hakan
  • Aslantas, Mustafa

Abstract

In this paper, we present a new approach to fractals through best proximity points, inspired by the remarkable relationship between fixed point theory and fractal theory. In this way, we introduce the concept of proximal IFS generated by a finite set of proximal contractions to expand the concept of IFS, one of the most common methods of creating fractals. Thus, as a new method of obtaining fractal we present a result showing that the proximal IFS has a unique best attractor under the certain conditions on metric spaces. To support our new result an illustrative example is given.

Suggested Citation

  • Altun, Ishak & Sahin, Hakan & Aslantas, Mustafa, 2021. "A new approach to fractals via best proximity point," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002034
    DOI: 10.1016/j.chaos.2021.110850
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    References listed on IDEAS

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    1. Chifu, Cristian & Petruşel, Adrian, 2008. "Multivalued fractals and generalized multivalued contractions," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 203-210.
    2. Ullah, Saif & Khan, Muhammad Altaf, 2020. "Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Atangana, Abdon & Khan, Muhammad Altaf, 2019. "Validity of fractal derivative to capturing chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 50-59.
    4. Naschie, M.S. El, 2006. "Fractal black holes and information," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 23-35.
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    Cited by:

    1. Yu, Dakuan & Ta, Wurui & Zhou, Youhe, 2021. "Fractal diffusion patterns of periodic points in the Mandelbrot set," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Zhao, Hongyu & Wang, Shengsheng & Fu, Zihao, 2024. "A new image encryption algorithm based on cubic fractal matrix and L-LCCML system," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    3. Anjum, Rizwan & Din, Muhammad & Zhou, Mi, 2024. "Fractals of two types of enriched (q,θ)-Hutchinson–Barnsley operators," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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