Stability of Cubic Functional Equation in IFN-Space and 2-Banach Space: Direct Method and Fixed-Point Approach

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DOI: https://doi.org/10.28924/2291-8639-24-2026-83
Published: Mar 19, 2026
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S. Gayathri, Siriluk Donganont, S. Karthick, Balaanandhan Radhakrishnan, Kandhasamy Tamilvanan, Stability of Cubic Functional Equation in IFN-Space and 2-Banach Space: Direct Method and Fixed-Point Approach, Int. J. Anal. Appl., 24 (2026), 83.

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S. Gayathri, Siriluk Donganont, S. Karthick, Balaanandhan Radhakrishnan, Kandhasamy Tamilvanan

Abstract

In this paper, the Hyers-Ulam stability of a cubic functional equation in finite-dimensional settings is examined in this study with particular attention to 2-Banach spaces and Intuitionistic Fuzzy Normed (IFN) spaces. We provide strong stability conditions for the cubic functional equation using both fixed-point approaches and direct methods. Our findings show that combinations of norm powers including sums and products may be used to efficiently manage the stability behavior. Moreover, given certain conditions, the related cubic mappings are guaranteed to be unique. We give specific instances that demonstrate the efficacy of our method in order to demonstrate the theoretical conclusions’ strength and application.

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