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We initiate the idea of a generalized Suzuki-type ( \(\alpha \) - \( \mathcal {Z} \) - \( \mathcal {G} \) )-contraction for two mappings utilizing a simulation function \(\zeta \) in b -metric space to establish the uniqueness of a common fixed point and coincidence point. Obtained outcomes generalize and broaden the conclusions of Antal et al. (J Nonlinear Sci Appl 13:212–222, 2022), Padcharoen et al. (Kragujevac J Math 42(3):419–430, 2018), Roldán-López-de-Hierro et al. (J Comput Appl Math 275:345–355, 2015), and many others existing in the literature. Our outcomes propose a new solution in a b-metric space to the response of a contractive mapping having a fixed point/common fixed at the point of discontinuity. Toward the end, we apply our outcomes to solve a system of integral equations.

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Application of Common Fixed Point in the Framework of  b -Metric Space via Simulation Function

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  • 发表日期：

    2025年

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  • Swati Antal,
  • Anita Tomar,
  • U. C. Gairola

摘要

We initiate the idea of a generalized Suzuki-type ( \(\alpha \) - \( \mathcal {Z} \) - \( \mathcal {G} \) )-contraction for two mappings utilizing a simulation function \(\zeta \) in b -metric space to establish the uniqueness of a common fixed point and coincidence point. Obtained outcomes generalize and broaden the conclusions of Antal et al. (J Nonlinear Sci Appl 13:212–222, 2022), Padcharoen et al. (Kragujevac J Math 42(3):419–430, 2018), Roldán-López-de-Hierro et al. (J Comput Appl Math 275:345–355, 2015), and many others existing in the literature. Our outcomes propose a new solution in a b-metric space to the response of a contractive mapping having a fixed point/common fixed at the point of discontinuity. Toward the end, we apply our outcomes to solve a system of integral equations.