STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C*-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE FUNCTIONAL EQUATION

摘要

In this article,we introduce the notion of generalized derivations on Hilbert C*-modules.We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equation rf(x+y/r)+sg(x-y/s)= 2h(x) for r,s ∈ R {0} on Hilbert C*-modules,where f,g,and h are mappings from a Hilbert C*-module M to M.