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...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2009-09, Vol.161 (6), p.792-802
Main Authors: Sidi Ammi, M. R., Torres, D. F. M.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-009-9600-2