Quantum integral inequalities on finite intervals

Journal of inequalities and applications

Jessada Tariboon¹ 

关键词: q-integral inequalities;    Hölder’s inequality;    Hermite-Hadamard’s inequality;    Ostrowski’s inequality;    Grüss-Čebyšev integral inequality;   

DOI  :  10.1186/1029-242X-2014-121

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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-Čebyšev 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). MSC: 34A08, 26D10, 26D15.

【 授权许可】

CC BY