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

Meng Liu, Meimei Song

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.

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How to Cite this Article:

Meng Liu, Meimei Song, Generalized stability of an AQ-functional equation in quasi-(2;p)-Banach spaces, Journal of Mathematical and Computational Science, Vol 6, No 5 (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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