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.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.
Cite this article
M. Liu, M. Song, Generalized stability of an AQ-functional equation in quasi-(2;p)-Banach spaces, J. Math. Comput. Sci. 6 (2016), 712–729.
BibTeX
@article{Liu2016,
author = {Liu, Meng and Song, Meimei},
title = {Generalized stability of an AQ-functional equation in quasi-(2;p)-Banach spaces},
journal = {J. Math. Comput. Sci.},
volume = {6},
year = {2016},
pages = {712--729},
doi = {}
}