The Hyers-Ulam stability of a functional equation deriving from quadratic and cubic functions in quasi-β-normed spaces

In this paper, we investigate the Hyers-Ulam stability of the following function equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 2f\left( {2x + y} \right) + 2f\left( {2x - y} \right) = 4f\left( {x + y} \right) + 4f\left( {x - y} \right) + 4f\left( {2x} \right) + f\left( {2y} \right) - 8f\left( x \right) - 8f\left( y \right) $$\end{document} in quasi-β-normed spaces.