Combined dynamic Grüss inequalities on time scales

We prove a more general version of the Grüss inequality by using the recent theory of combined dynamic derivatives on time scales and the more general notions of diamond- α derivative and integral. For the particular case where α = 1, one obtains the delta-integral Grüss inequality on time scales in (see M. Bohner and T. Matthews [ 5 ]); for α = 0 a nabla-integral Grüss inequality is derived. If we further restrict ourselves by fixing the time scale to the real (or integer) numbers, then the standard continuous (discrete) inequalities are obtained.