English

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}
}

Comments

9 pages

R2 v1 2026-06-21T10:02:12.469Z