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Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space

Author

Listed:
  • Nesrin Manav Tatar

    (Department of Mathematics, Erzincan Binali Yildirim University, Erzincan 24002, Turkey)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA)

Abstract

In the realm of generalized modular metric spaces, we substantiate the validity of fixed-point theorems with Branciari contractions. This paper expands and broadens the original theorems in this context. Subsequently, by building upon this foundation, we explore various integral contractions to identify and characterize fixed points within this context. To highlight the practical implications of our work, we introduce the concept of the best proximity pair, thereby culminating in the best approximation theorem. We apply this theoretical construct to a specific example—one that is guided by the best approximation method described in prior research.

Suggested Citation

  • Nesrin Manav Tatar & Ravi P. Agarwal, 2023. "Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4455-:d:1269029
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    References listed on IDEAS

    as
    1. A. Branciari, 2002. "A fixed point theorem for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    2. Naveen Mani & Amit Sharma & Rahul Shukla & Jozef Banas, 2023. "Fixed Point Results via Real-Valued Function Satisfying Integral Type Rational Contraction," Abstract and Applied Analysis, Hindawi, vol. 2023, pages 1-6, January.
    3. P. Vijayaraju & B. E. Rhoades & R. Mohanraj, 2005. "A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-6, January.
    4. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
    Full references (including those not matched with items on IDEAS)

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