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Generalized Wardowski type contractive mappings in b-metric spaces and some fixed point results with applications in optimization problem and modeling biological ecosystem

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  • Maryam Iqbal
  • Afshan Batool
  • Aftab Hussain
  • Hamed Al Sulami

Abstract

In the realm of b-metric spaces, this study introduces a novel generalized Wardowski-type quasi-contraction, denoted as β-(θ, ϑ). We begin by applying this new contraction to derive standard fixed point results. Subsequently, we establish the existence of a generalized quasi-contraction of the Wardowski type, thereby validating the robustness of our findings. Specifically, we utilize Nadler’s work to model biological ecosystems and apply our results to solve an optimization problem. To illustrate the practical implications and effectiveness of our approach, we provide a comparative analysis between our results and those of Nadler. This comprehensive study underscores the significance and utility of our generalized contraction in both theoretical and applied contexts.

Suggested Citation

  • Maryam Iqbal & Afshan Batool & Aftab Hussain & Hamed Al Sulami, 2024. "Generalized Wardowski type contractive mappings in b-metric spaces and some fixed point results with applications in optimization problem and modeling biological ecosystem," PLOS ONE, Public Library of Science, vol. 19(12), pages 1-16, December.
    • Handle: RePEc:plo:pone00:0313033
    DOI: 10.1371/journal.pone.0313033
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    References listed on IDEAS

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    1. Piyachat Borisut & Poom Kumam & Vishal Gupta & Naveen Mani, 2019. "Generalized ( ψ , α , β )—Weak Contractions for Initial Value Problems," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    2. Aftab Hussain & Huseyin Isik, 2021. "Solution of Fractional Differential Equations Utilizing Symmetric Contraction," Journal of Mathematics, Hindawi, vol. 2021, pages 1-17, May.
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