فهرست نشریات علمی دسترسی آزاد ایران

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.