Asymptotic behavior of a radical quadratic functional equation in quasi-β-Banach spaces

	Asymptotic behavior of a radical quadratic functional equation in quasi-β-Banach spaces
International Journal of Nonlinear Analysis and Applications
مقاله 10، دوره 14، شماره 3، خرداد 2023، صفحه 113-120 اصل مقاله (372.14 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23897.2634
نویسندگان
Muaadh Almahalebi^* ¹؛ Abdellatif Chahbi²
¹Department of Mathematics, Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
²Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Agadir, Morocco
چکیده
Let $\mathbb{R}$ be the set of real numbers and $\big(Y,\\|\cdot\\|\big)$ be a real quasi-$\beta$-Banach space. In this paper, we prove the Hyers-Ulam stability on a restricted domain in quasi-$\beta$-spaces for the following two radical functional equations $$ f\big(\sqrt{x^{2}+y^{2}}\big)=f(x)+f(y) $$ and $$ f\big(\sqrt{x^{2}+y^{2}}\big)=g(x)+f(y) $$ where $f,g:\mathbb{R}\to Y$. Also, we discuss an asymptotic behavior for these equations.
کلیدواژه‌ها
radical functional equation؛ Hyers-Ulam stability؛ quasi-β-normed spaces؛ restricted domain
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