Solution and Stability of Euler-Lagrange-Rassias Quartic Functional Equations in Various Quasinormed Spaces

Abstract

We obtain the general solution of Euler-Lagrange-Rassias quartic functional equation of the following $f\left(ax+by\right)+f\left(bx+ay\right)+(\mathrm{1}/\mathrm{2})ab(a-b{)}^{\mathrm{2}}f(x-y)=(a^{\mathrm{2}}-b^{\mathrm{2}}{)}^{\mathrm{2}}\left[f\left(x\right)+f\left(y\right)\right]+(\mathrm{1}/\mathrm{2})ab(a+b{)}^{\mathrm{2}}f(x+y)\mathrm{}$. We also prove the Hyers-Ulam-Rassias stability in various quasinormed spaces when $b=\mathrm{1}\mathrm{}$.