Generalized Stability of Euler-Lagrange Quadratic Functional Equation

Abstract

The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equation $f(ax+by)+af(x-by)=(a+1)b^{2}f(y)+a(a+1)f(x)$, in $(\beta ,p)$-Banach space, where $a,b$ are fixed rational numbers such that $a\ne -\mathrm{1,0}$ and $b\ne 0$.