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Fractals in Product Fuzzy Metric Space

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Fractals, Wavelets, and their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 92))

Abstract

The purpose of this paper is to prove the Hutchinson–Barnsley operator on the product fuzzy metric space is fuzzy B-contraction. We also present the fuzzy B-contraction properties of HB operator in product fuzzy metric space. The notion of product fuzzy fractal is introduced in product fuzzy metric space in the sense of the fuzzy B-contraction.

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Acknowledgements

The research work has been supported by University Grants Commission, Government of India, New Delhi, India under the schemes of UGC—Major Research Project with Grant No.: F.No. 42-21/2013 (SR)/dated 12.03.2013 and UGC—Special Assistance Programme (DRS-II).

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Authors and Affiliations

  1. Department of Mathematics, The Gandhigram Rural Institute - Deemed University, Gandhigram, 624 302, Dindigul, Tamil Nadu, India

    R. Uthayakumar & A. Gowrisankar

Authors
  1. R. Uthayakumar
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  2. A. Gowrisankar
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Corresponding author

Correspondence to A. Gowrisankar .

Editor information

Editors and Affiliations

  1. Institut für Mathematik und Informatik, Universität Greifswald, Greifswald, Mecklenburg-Vorpomm., Germany

    Christoph Bandt

  2. Mathematical Sciences Institute, Australian National University, Canberra, Australia

    Michael Barnsley

  3. Math Department, Boston University, Boston, Massachusetts, USA

    Robert Devaney

  4. Mathematical Institute, University of St Andrews, St Andrews, Fife, United Kingdom

    Kenneth J. Falconer

  5. Department of Mathematics and Statistics, University of Hyderabad, Hyderabad, India

    V. Kannan

  6. Department of Basic Sciences & Humanities, Rajagiri School of Engineering & Technology, Kerala, India

    Vinod Kumar P.B.

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Uthayakumar, R., Gowrisankar, A. (2014). Fractals in Product Fuzzy Metric Space. In: Bandt, C., Barnsley, M., Devaney, R., Falconer, K., Kannan, V., Kumar P.B., V. (eds) Fractals, Wavelets, and their Applications. Springer Proceedings in Mathematics & Statistics, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-08105-2_9

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