Generalized stability of an AQ-functional equation in quasi-(2;p)-Banach spaces

Abstract

In this paper, we introduce and investigate the general solution of a new functional equation

$$

f(\frac{x+y}{a}+\frac{z+w}{b})+f(\frac{x+y}{a}-\frac{z+w}{b})&=&\frac{1}{a^{2}}[(1+a)f(x+y)+(1-a)f(-x-y)]\\

&+&\frac{1}{b^{2}}[f(z+w)+f(-z-w)]

$$

where $a,b\geq 1$ and discuss its Generalized Hyers-Ulam-Rassias stability under the conditions such as even, odd, approximately even and approximately odd in quasi-(2;p)-Banach spaces.