Quantum integral inequalities on finite intervals

Abstract

In this paper, some of the most important integral inequalities of analysis are extended to quantum calculus. These include the Hölder, Hermite-Hadamard, trapezoid, Ostrowski, Cauchy-Bunyakovsky-Schwarz, Grüss, and Grüss- ? Cebyŝev integral inequalities. The analysis relies on the notions of q-derivative and q-integral on finite intervals introduced by the authors in (Tariboon and Ntouyas in Adv. Differ. Equ. 2013:282, 2013). © 2014 Tariboon and Ntouyas; licensee Springer.