Stability problem of Ulam for generalized forms of Cauchy functional equation

[摘要] Let G I be a vector space and G(2) a Banach space. In this paper, we solve the generalized FlyersUlam-Rassias stability problem for a generalized form g(Sigma(i=1)(n)a(i)x(i) + c) = Sigma(i=1)(n)A(i)g(x(i)) + C, for all x(i) is an element of G(1), of Cauchy functional equation f(x + y) = f(x) + f(y) for a mapping f : G(1) -> G(2), where a(i), A(i) are scalars for all i = 1,..., n and c is an element of G(1), C is an element of G(2) are vectors. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2005-12-15

[关键词] Ulam stability problem;square-symmetric;Cauchy functional equation