ADDITIVE FUNCTIONAL INEQUALITIES AND DERIVATIONS ON HILBERT C*-MODULES

Abstract

AbstractIn this paper we investigate the following functional inequality $ \begin{eqnarray*} \| f(x-y-z) - f(x-y+z) + f(y) +f(z)\| \leq \|f(x+y-z) - f(x)\| \end{eqnarray*}$ in Banach spaces, and employing the above inequality we prove the generalized Hyers–Ulam stability of derivations in Hilbert C*-modules.