Stability for quadratic functional equation in the spaces of generalized functions

[摘要] In this paper, we consider the general solution of quadratic functional equation f(ax + y)+f(ax - y) = f(x + y) + f(x - y) + 2(a(2) - 1)f(x) for any integer a with a not equal -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 C generalized Hyers-Ulam stability originated from the Th.M. Rassias's stability theorem that appeared in his paper (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-01

[关键词] quadratic functional equation;Hyers-Ulam-Rassias stability;distribution;heat kernel;Gauss transform