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

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 equationsf\big(\sqrt{x^{۲}+y^{۲}}\big)=f(x)+f(y)and f\big(\sqrt{x^{۲}+y^{۲}}\big)=g(x)+f(y)where f,g:\mathbb{R}\to Y. Also, we discuss an asymptotic behavior for these equations.

Keywords:

radical functional equation , Hyers-Ulam stability , quasi-β-normed spaces , restricted domain