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Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

Author

Listed:
  • Hasanen A. Hammad

    (Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt)

  • Manuel De la Sen

    (Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Spain)

Abstract

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

Suggested Citation

  • Hasanen A. Hammad & Manuel De la Sen, 2021. "Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces," Mathematics, MDPI, vol. 9(18), pages 1-23, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2267-:d:635983
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    References listed on IDEAS

    as
    1. Saif Ur Rehman & Ronnason Chinram & Chawalit Boonpok & Ali Jaballah, 2021. "Rational Type Fuzzy-Contraction Results in Fuzzy Metric Spaces with an Application," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, April.
    2. Binayak S. Choudhury & Erdal Karapınar & Amaresh Kundu, 2012. "Tripled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-14, July.
    3. Anil Kumar & Savita Rathee & Navin Kumar, 2013. "The Point of Coincidence and Common Fixed Point for Three Mappings in Cone Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, June.
    4. Hasanen Abuelmagd Hammad & Manuel De la Sen, 2019. "A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations," Mathematics, MDPI, vol. 7(7), pages 1-18, July.
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    Cited by:

    1. Hasanen A. Hammad & Manuel De la Sen, 2022. "Application to Lipschitzian and Integral Systems via a Quadruple Coincidence Point in Fuzzy Metric Spaces," Mathematics, MDPI, vol. 10(11), pages 1-16, June.

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