Refined stability of the additive, quartic and sextic functional equations with counter-examples

Hasanen A. Hammad; Hassen Aydi; Manuel De la Sen

doi:10.3934/math.2023736

Refined stability of the additive, quartic and sextic functional equations with counter-examples

Hasanen A. Hammad^*, Hassen Aydi^*, Manuel De la Sen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this study, we utilize the direct method (Hyers approach) to examine the refined stability of the additive, quartic, and sextic functional equations in modular spaces with and without the ∆₂-condition. We also use the direct approach to discuss the Ulam stability in 2-Banach spaces. Ultimately, we ensure that stability of above equations does not hold in a particular scenario by utilizing appropriate counter-examples.

Original language	English
Pages (from-to)	14399-14425
Number of pages	27
Journal	AIMS Mathematics
Volume	8
Issue number	6
DOIs	https://doi.org/10.3934/math.2023736
Publication status	Published - 2023
Externally published	Yes

Keywords

2-Banach space
additive
modular space
quartic and sextic functional equations
refined stability

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10.3934/math.2023736

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abstract = "In this study, we utilize the direct method (Hyers approach) to examine the refined stability of the additive, quartic, and sextic functional equations in modular spaces with and without the ∆2-condition. We also use the direct approach to discuss the Ulam stability in 2-Banach spaces. Ultimately, we ensure that stability of above equations does not hold in a particular scenario by utilizing appropriate counter-examples.",

keywords = "2-Banach space, additive, modular space, quartic and sextic functional equations, refined stability",

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AB - In this study, we utilize the direct method (Hyers approach) to examine the refined stability of the additive, quartic, and sextic functional equations in modular spaces with and without the ∆2-condition. We also use the direct approach to discuss the Ulam stability in 2-Banach spaces. Ultimately, we ensure that stability of above equations does not hold in a particular scenario by utilizing appropriate counter-examples.

KW - 2-Banach space

KW - additive

KW - modular space

KW - quartic and sextic functional equations

KW - refined stability

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Refined stability of the additive, quartic and sextic functional equations with counter-examples

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Keywords

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