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Generalized enriched cyclic contractions with application to generalized iterated function system

Author

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  • Abbas, Mujahid
  • Anjum, Rizwan
  • Iqbal, Hira

Abstract

The purpose of this article is to initiate a new class of cyclic contraction mappings and establish a related fixed point theorem in the framework of a Banach space. To approximate the fixed point, a convergence theorem employing the Krasnoselskij iteration is presented for which a priori and a posterior error estimates are also determined. These results modify and extend several comparable results in the existing literature. As an application, we investigate the iterated function system (IFS) comprised of generalized cyclic contraction mappings. Some examples are also presented to validate the results.

Suggested Citation

  • Abbas, Mujahid & Anjum, Rizwan & Iqbal, Hira, 2022. "Generalized enriched cyclic contractions with application to generalized iterated function system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009450
    DOI: 10.1016/j.chaos.2021.111591
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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. Mujahid Abbas & Manuel De la Sen & Talat Nazir, 2015. "Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-10, July.
    3. Maryam A. Alghamdi & Vasile Berinde & Naseer Shahzad, 2013. "Fixed Points of Multivalued Nonself Almost Contractions," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, July.
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    Cited by:

    1. Rizwan Anjum & Andreea Fulga & Muhammad Waqar Akram, 2023. "Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions," Mathematics, MDPI, vol. 11(22), pages 1-11, November.
    2. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(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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