Title: Diamond-alpha Gruess type inequalities on time scales

Authors: Martin Bohner, Thomas Matthews, Adnan Tuna

Addresses: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA. ' Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA. ' Faculty of Science and Arts, Department of Mathematics, University of Nigde, Merkez, 51240, Nigde, Turkey

Abstract: In this paper, we study a more general version of Gruss type inequalities on time scales by using the recent theory of combined dynamic derivatives on time scales. In the case α = 1, we obtain delta-integral Gruss type inequalities on time scales. For α = 0, we obtain nabla-integral Gruss type inequalities. We supply numerous examples throughout.

Keywords: Gruess type inequality; diamond-alpha; combined dynamic derivatives; time scales; nabla integral; delta integral.

DOI: 10.1504/IJDSDE.2011.038504

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.234 - 247

Published online: 09 Feb 2011 *

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