### 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.**How to Cite this Article:**Meng Liu, Meimei Song, Generalized stability of an AQ-functional equation in quasi-(2;p)-Banach spaces, J. Math. Comput. Sci., 6 (2016), 712-729 Copyright © 2016 Meng Liu, Meimei Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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