Stability of quadratic functional equation in modular spaces

In this paper, we study the Hyers-Ulam stability of the following equation \begin{multline*} \phi(x+y-z)+\phi(x+z-y)+\phi(y+z-x)=\phi (x-y)+\phi(x-z)+\phi(z-y) +\phi(x)+\phi(y) +\phi(z) \end{multline*} in modular space, with or without $\Delta_2$-condition, and in $\beta$-homogeneous Banach space.

Publication Details

Journal
ArXiv.org
Published
2025-04-12
Primary Topic
Functional Equations Stability Results
Type
article
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article

Stability of quadratic functional equation in modular spaces

ArXiv.org
Functional Equations Stability Results
article

Stability of quadratic functional equation in modular spaces

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Abstract

In this paper, we study the Hyers-Ulam stability of the following equation \begin{multline*} \phi(x+y-z)+\phi(x+z-y)+\phi(y+z-x)=\phi (x-y)+\phi(x-z)+\phi(z-y) +\phi(x)+\phi(y) +\phi(z) \end{multline*} in modular space, with or without $\Delta_2$-condition, and in $\beta$-homogeneous Banach space.

ArXiv.org
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Functional Equations Stability Results
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Stability of quadratic functional equation in modular spaces · ArXiv.org (2025) | TGRS Research Map | TGRS