Stability of Cauchy additive functional equation in fuzzy Banach spaces

Kim, Hark-Mahn; Chang, Ick-Soon; Son, Eunyoung

doi:10.7153/mia-16-87

Cited by 6 publications

(2 citation statements)

References 16 publications

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“…In 2013, Kim [21] investigated the stability of the additive functional equation in fuzzy Banach spaces. Motivated by the method and direction of research of Kim [21], an effort has been made here to investigate the stability of the additive functional equation…”

Section: Stability Results Of Additive Functional Equationmentioning

confidence: 99%

Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces

Tamilvanan¹,

Alkhaldi

Jakhar

et al. 2023

Mathematics

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In this work, we investigate the refined stability of the additive, quartic, and quintic functional equations in modular spaces with and without the Δ2-condition using the direct method (Hyers method). We also examine Ulam stability in 2-Banach space using the direct method. Additionally, using a suitable counterexample, we eventually demonstrate that the stability of these equations fails in a certain case.

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Section: Stability Results Of Additive Functional Equationmentioning

confidence: 99%

Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces

Tamilvanan¹,

Alkhaldi

Jakhar

et al. 2023

Mathematics

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show abstract

“…in random normed spaces was studied by Mihet et al [24]. Kim et al [25] proposed a generalised version of CFE, as follows:…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

et al. 2022

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In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated.

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Stability of various functional equations in non-Archimedean $$(n,\beta )$$-normed spaces

Jyotsana

Chugh

Jaiswal

et al. 2022

J Anal

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Stability of Cauchy additive functional equation in fuzzy Banach spaces

Abstract: Abstract. In this article, we prove the generalized Hyers-Ulam stability of the following Cauchy additive functional equationin fuzzy Banach spaces for any fixed nonzero integer n .Mathematics subject classification (2010): 39B52, 46S40.

Cited by 6 publications

References 16 publications

Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces

Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

Stability of various functional equations in non-Archimedean $$(n,\beta )$$-normed spaces

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