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Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces

Author

Listed:
  • P. Saha

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India)

  • T. K. Samanta

    (Department of Mathematics, Uluberia College, Uluberia, Howrah, West Bengal 711315, India)

  • Pratap Mondal

    (Department of Mathematics, Bijoy Krishna Girls’ College, Howrah, Howrah, West Bengal 711101, India)

  • B. S. Choudhury

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India)

  • Manuel De La Sen

    (Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, Campus of Leioa, Bizkaia, 48940 Leioa, Spain)

Abstract

In this paper we investigate Hyers-Ulam-Rassias stability of certain nonlinear functional equations. Considerations of such stabilities in different branches of mathematics have been very extensive. Again the fuzzy concepts along with their several extensions have appeared in almost all branches of mathematics. Here we work on intuitionistic fuzzy real Banach spaces, which is obtained by combining together the concepts of fuzzy Banach spaces with intuitionistic fuzzy sets. We establish that pexiderized quadratic functional equations defined on such spaces are stable in the sense of Hyers-Ulam-Rassias stability. We adopt a fixed point approach to the problem. Precisely, we use a generxalized contraction mapping principle. The result is illustrated with an example.

Suggested Citation

  • P. Saha & T. K. Samanta & Pratap Mondal & B. S. Choudhury & Manuel De La Sen, 2020. "Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:974-:d:371522
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    References listed on IDEAS

    as
    1. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    2. Soon-Mo Jung, 2000. "Quadratic functional equations of Pexider type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-9, January.
    3. George Isac & Themistocles M. Rassias, 1996. "Stability of ψ -additive mappings: applications to nonlinear analysis," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-10, January.
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    Cited by:

    1. P. Agilan & Mohammed M. A. Almazah & K. Julietraja & Ammar Alsinai, 2023. "Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces," Mathematics, MDPI, vol. 11(3), pages 1-19, January.

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