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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 | ||
| تاریخ دریافت: 16 اردیبهشت 1400، تاریخ بازنگری: 12 تیر 1400، تاریخ پذیرش: 23 تیر 1400 | ||
| 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 | ||
| مراجع | ||
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