Generalizations of some q-integral inequalities of Hölder, Ostrowski and Grüss type

Abstract

This paper investigates some well-known inequalities for $ q $-$ h $-integrals. These include Hölder, Ostrowski, Grüss and Opial type inequalities. Refinement of the Hadamard inequality for $ q $-$ h $-integrals is also established by applying the definition of strongly convex functions. From main theorems, $ q $-Hölder, $ q $-Ostrowski and $ q $-Grüss inequalities can be obtained in particular cases.

Keywords

• $ q $-integral
• $ q $-$ h $-integral
• hölder inequality
• ostrowski inequality
• güss inequality
• hadamard inequality