Stability problem of Ulam for generalized forms of Cauchy functional equation

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Abstract

Let G1 be a vector space and G2 a Banach space. In this paper, we solve the generalized Hyers–Ulam–Rassias stability problem for a generalized form g(i=1naixi+c)=i=1nAig(xi)+C,xiG1, of Cauchy functional equation f(x+y)=f(x)+f(y) for a mapping f:G1G2, where ai,Ai are scalars for all i=1,,n and cG1, CG2 are vectors.

Keywords

Ulam stability problem
Square-symmetric
Cauchy functional equation

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This work was supported by grant No. R01-2000-000-00005-0(2004) from the KOSEF.