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Multi Fractals of Generalized Multivalued Iterated Function Systems in b -Metric Spaces with Applications

Author

Listed:
  • Sudesh Kumari

    (Department of Mathematics, Government College for Girls Sector 14, Gurugram 122001, India
    These authors contributed equally to this work.)

  • Renu Chugh

    (Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India
    These authors contributed equally to this work.)

  • Jinde Cao

    (Research Center for Complex Systems and Network Sciences, School of Mathematics, Southeast University, Nanjing 210096, China
    These authors contributed equally to this work.)

  • Chuangxia Huang

    (School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, China
    These authors contributed equally to this work.)

Abstract

In this paper, we obtain multifractals (attractors) in the framework of Hausdorff b -metric spaces. Fractals and multifractals are defined to be the fixed points of associated fractal operators, which are known as attractors in the literature of fractals. We extend the results obtained by Chifu et al. (2014) and N.A. Secelean (2015) and generalize the results of Nazir et al. (2016) by using the assumptions imposed by Dung et al. (2017) to the case of ciric type generalized multi-iterated function system (CGMIFS) composed of ciric type generalized multivalued G -contractions defined on multifractal space C ( U ) in the framework of a Hausdorff b -metric space, where U = U 1 × U 2 × ⋯ × U N , N being a finite natural number. As an application of our study, we derive collage theorem which can be used to construct general fractals and to solve inverse problem in Hausdorff b -metric spaces which are more general spaces than Hausdorff metric spaces.

Suggested Citation

  • Sudesh Kumari & Renu Chugh & Jinde Cao & Chuangxia Huang, 2019. "Multi Fractals of Generalized Multivalued Iterated Function Systems in b -Metric Spaces with Applications," Mathematics, MDPI, vol. 7(10), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:967-:d:276200
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    References listed on IDEAS

    as
    1. Dejan Ilić & Mujahid Abbas & Talat Nazir, 2015. "Iterative approximation of fixed points of Prešić operators on partial metric spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 288(14-15), pages 1634-1646, October.
    2. Chuangxia Huang & Jie Cao & Peng Wang, 2016. "Attractor and Boundedness of Switched Stochastic Cohen-Grossberg Neural Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-19, May.
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    Cited by:

    1. Kumari, Sudesh & Gdawiec, Krzysztof & Nandal, Ashish & Postolache, Mihai & Chugh, Renu, 2022. "A novel approach to generate Mandelbrot sets, Julia sets and biomorphs via viscosity approximation method," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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