Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4621934 | Journal of Mathematical Analysis and Applications | 2007 | 10 Pages |
Abstract
In this paper, we consider the general solution of quadratic functional equationf(ax+y)+f(ax−y)=f(x+y)+f(x−y)+2(a2−1)f(x)f(ax+y)+f(ax−y)=f(x+y)+f(x−y)+2(a2−1)f(x) for any integer a with a≠−1,0,1a≠−1,0,1. Moreover we reformulate and prove the Hyers–Ulam–Rassias stability theorem of the above equation in the spaces of tempered distributions and Fourier hyperfunctions. The generalized Hyers–Ulam stability originated from the Th.M. Rassias's stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297–300].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Young-Su Lee, Soon-Yeong Chung,