Combined dynamic Gruss inequalities on time scales

Details Combined dynamic Gruss inequalities on time scales Combined dynamic Gruss inequalities on time scales

2008-01-11

arxiv.org/abs/0801.1865v1

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.

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