Páles Z, Volkmann P, Luce R D
Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf. 12, Hungary.
Proc Natl Acad Sci U S A. 1998 Oct 27;95(22):12772-5. doi: 10.1073/pnas.95.22.12772.
The stability of the functional equation f(x composite function y) = H(f(x), f(y)) (x, y in S) is investigated, where H is a homogeneous function and composite function is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.
研究了函数方程(f(x\circ y)=H(f(x),f(y)))（(x,y\in S)）的稳定性，其中(H)是一个齐次函数，且(\circ)是集合(S)上的平方对称运算。给出的结果包括并推广了1941年获得的关于柯西函数方程稳定性的经典海尔定理。
