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Some Results in Fuzzy b -Metric Space with b -Triangular Property and Applications to Fredholm Integral Equations and Dynamic Programming

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Listed:
  • Gunaseelan Mani

    (Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamil Nadu, India)

  • Arul Joseph Gnanaprakasam

    (Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Tamil Nadu, India)

  • Liliana Guran

    (Department of Pharmaceutical Sciences, “Vasile Goldiş” Western University of Arad, L. Rebreanu Street, No. 86, 310048 Arad, Romania)

  • Reny George

    (Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

  • Zoran D. Mitrović

    (Faculty of Electrical Engineering, University of Banja Luka, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina)

Abstract

In this paper, we introduce the b -triangular property in fuzzy b -metric space. Furthermore, we give some new fixed point results in fuzzy b -metric space for non-continuous mappings. Our results generalize and expand some results from the related literature. Two applications of our results, to solving Fredholm integral equation and in dynamic programming, are also given.

Suggested Citation

  • Gunaseelan Mani & Arul Joseph Gnanaprakasam & Liliana Guran & Reny George & Zoran D. Mitrović, 2023. "Some Results in Fuzzy b -Metric Space with b -Triangular Property and Applications to Fredholm Integral Equations and Dynamic Programming," Mathematics, MDPI, vol. 11(19), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4101-:d:1249688
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    References listed on IDEAS

    as
    1. Richard Bellman, 1954. "On some applications of the theory of dynamic programming to logistics," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(2), pages 141-153, June.
    2. Dušan Rakić & Tatjana Došenović & Zoran D. Mitrović & Manuel de la Sen & Stojan Radenović, 2020. "Some Fixed Point Theorems of Ćirić Type in Fuzzy Metric Spaces," Mathematics, MDPI, vol. 8(2), pages 1-15, February.
    3. Richard Bellman, 1954. "Some Applications of the Theory of Dynamic Programming---A Review," Operations Research, INFORMS, vol. 2(3), pages 275-288, August.
    4. Weiquan Zhang & Dong Qiu & Zhifeng Li & Gangqiang Xiong, 2012. "Common Fixed Point Theorems in a New Fuzzy Metric Space," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, February.
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