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arXiv · 2203.03114

Ulam stability of an additive-quadratic functional equation in F-space and quasi-Banach spaces

Linlin Fu·Qi Liu·Yongjin Li
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Abstract

By adopting the direct method and fixed point method, we prove that the Hyers-Ulam stability of the following additive-quadratic functional equation \begin{equation} f(x+y, z+w)+f(x-y, z-w)-2 f(x, z)-2 f(x, w)=0 \end{equation} in $\beta$-homogeneous $F$-spaces and quasi-Banach spaces. There are some differences that we consider the target space with the $\beta$-homogeneous norm and quasi-norm. Overcoming the $\beta$-homogeneous norm and quasi-norm bottlenecks, we get some new results.

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Linlin Fu, Qi Liu, Yongjin Li. 2022-03-07. Ulam stability of an additive-quadratic functional equation in F-space and quasi-Banach spaces. https://arxiv.org/abs/2203.03114

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