具有平方对称运算的函数方程的赫尔斯 - 乌拉姆稳定性。
Hyers-ulam stability of functional equations with a square-symmetric operation.
作者信息
Páles Z, Volkmann P, Luce R D
机构信息
Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf. 12, Hungary.
出版信息
Proc Natl Acad Sci U S A. 1998 Oct 27;95(22):12772-5. doi: 10.1073/pnas.95.22.12772.
Abstract
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.
摘要
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。
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