科研之友
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摘要
Let S and G be a commutative semigroup and a commutative group, respectively, C and R+ the sets of complex numbers and nonnegative real numbers, respectively, and S -> S or sigma : G -> G an involution. In this paper, we first investigate general solutions of the functional equation f(x + sigma y) = f (x)g(y) - g(x)f(y) for all x, y epsilon S, where f, g : S -> C. We then prove the Hyers-Ulamstability of the functional equation; that is, we study the functional inequality vertical bar f(x + sigma y) - f(x)g(y) + g(x)f(y)vertical bar| <= psi(y) for all x, y epsilon G, where f, g : G -> C and psi : G -> R+.
- 出版日期2015
