Orthogonal Stability of Additive Functional Equation in Fuzzy β-Normed Spaces

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DOI: https://doi.org/10.28924/2291-8639-22-2024-231
Published: Dec 9, 2024
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M. Nila, A. Vijayalakshmi, M. Balamurugan, S. Gayathri, K. Thangapandi, K. Punniyamoorthy, N. Prabaharan, Orthogonal Stability of Additive Functional Equation in Fuzzy β-Normed Spaces, Int. J. Anal. Appl., 22 (2024), 231.

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M. Nila, A. Vijayalakshmi, M. Balamurugan, S. Gayathri, K. Thangapandi, K. Punniyamoorthy, N. Prabaharan

Abstract

The primary objective of this study is to present a novel form of generalised additive functional equation \(\phi\Big(\sum_{j=1}^{l}j v_{j}\Big)=\sum_{j=1}^{l}j \phi(v_{j}),\) where \(l\geq 2\) with each \(v_{i}\bot v_{j};~ i \neq j =1,2,\cdots,l,\) and derive its solution. Mainly, we examine the Hyers-Ulam-Rassias orthogonal stability of this equation by utilizing two different approaches.

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