  Let X be a Hilbert C^*-module on C^*-algebra A and p in A. We denote by
Dp(A;X) the set of all continuous functions f on A, which are Frechet
differentiable on a open neighborhood U of p. Then, we introduce some
generalized semi-inner products on Dp(A;X), and using them some Gruss type
inequalities in semi-inner product C^*-module Dp(A;X) and Dp(A;X^n) are
established.
