Mathematics – Classical Analysis and ODEs
Scientific paper
2008-01-11
Journal of Mathematical Sciences, Vol. 161, No. 6, 2009, 792--802
Mathematics
Classical Analysis and ODEs
9 pages
Scientific paper
10.1007/s10958-009-9600-2
We prove a more general version of the Gruss inequality by using the recent theory of combined dynamic derivatives on time scales and the more general notions of diamond-alpha derivative and integral. For the particular case when alpha = 1, one gets a delta-integral Gruss inequality on time scales; for alpha = 0 a nabla-integral Gruss inequality. If we further restrict ourselves by fixing the time scale to the real (or integer) numbers, then the standard continuous (discrete) inequalities are obtained.
Sidi Ammi Moulay Rchid
Torres Delfim F. M.
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