Stability of Quartic Functional Equation in Non-Archimedean IFN-Spaces

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DOI: https://doi.org/10.28924/2291-8639-23-2025-194
Published: Aug 15, 2025
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Kandhasamy Tamilvanan, Siriluk Donganont, Balaanandhan Radhakrishnan, John Michael Rassias, Stability of Quartic Functional Equation in Non-Archimedean IFN-Spaces, Int. J. Anal. Appl., 23 (2025), 194.

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Kandhasamy Tamilvanan, Siriluk Donganont, Balaanandhan Radhakrishnan, John Michael Rassias

Abstract

In this work, we focus on the non-Archimedean intuitionistic fuzzy normed framework, specifically on the generalized Ulam stability of quartic functional equations. By combining direct approaches with advanced fixed-point techniques, we prove that quartic-type mappings exist, are unique, and stable, providing strong extensions of Hyers-Ulam-Rassias stability. We present a new method for studying stability phenomena in abstract nonlinear systems and fulfill a gap between fuzzy analysis and non-Archimedean normed structures. Future applications in computational mathematics, fuzzy modeling, and uncertain systems analysis will benefit from these insights, which strengthen the theoretical framework.

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