Combined dynamic Gruss inequalities on time scales
Classical Analysis and ODEs
2009-09-18 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0801.1865,
title = {Combined dynamic Gruss inequalities on time scales},
author = {Moulay Rchid Sidi Ammi and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:0801.1865},
year = {2009}
}
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9 pages