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Iterative Schemes Involving Several Mutual Contractions

Author

Listed:
  • María A. Navascués

    (Departamento de Matemática Aplicada, Escuela de Ingeniería y Arquitectura, Universidad de Zaragoza, 50018 Zaragoza, Spain)

  • Sangita Jha

    (Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, India)

  • Arya K. B. Chand

    (Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India)

  • Ram N. Mohapatra

    (Department of Mathematics, University of Central Florida, Orlando, FL 32817, USA)

Abstract

In this paper, we introduce the new concept of mutual Reich contraction that involves a pair of operators acting on a distance space. We chose the framework of strong b-metric spaces (generalizing the standard metric spaces) in order to add a more extended underlying structure. We provide sufficient conditions for two mutually Reich contractive maps in order to have a common fixed point. The result is extended to a family of operators of any cardinality. The dynamics of iterative discrete systems involving this type of self-maps is studied. In the case of normed spaces, we establish some relations between mutual Reich contractivity and classical contractivity for linear operators. Then, we introduce the new concept of mutual functional contractivity that generalizes the concept of classical Banach contraction, and perform a similar study to the Reich case. We also establish some relations between mutual functional contractions and Banach contractivity in the framework of quasinormed spaces and linear mappings. Lastly, we apply the obtained results to convolutional operators that had been defined by the first author acting on Bochner spaces of integrable Banach-valued curves.

Suggested Citation

  • María A. Navascués & Sangita Jha & Arya K. B. Chand & Ram N. Mohapatra, 2023. "Iterative Schemes Involving Several Mutual Contractions," Mathematics, MDPI, vol. 11(9), pages 1-18, April.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2019-:d:1131445
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    References listed on IDEAS

    as
    1. Ram N. Mohapatra & María A. Navascués & María V. Sebastián & Saurabh Verma, 2022. "Iteration of Operators with Contractive Mutual Relations of Kannan Type," Mathematics, MDPI, vol. 10(15), pages 1-14, July.
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    Cited by:

    1. Alexander Šostak & Tarkan Öner & İlyas Can Duman, 2023. "On Topological and Metric Properties of ⊕-sb-Metric Spaces," Mathematics, MDPI, vol. 11(19), pages 1-12, September.
    2. Navascués, M.A., 2024. "Approximation of fixed points and fractal functions by means of different iterative algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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    1. Navascués, M.A., 2024. "Approximation of fixed points and fractal functions by means of different iterative algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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