New Perspectives of Symmetry Conferred by <i>q</i>-Hermite-Hadamard Type Integral Inequalities

Abstract

The main goal of this work is to provide quantum parametrized Hermite-Hadamard like type integral inequalities for functions whose second quantum derivatives in absolute values follow different type of convexities. A new quantum integral identity is derived for twice quantum differentiable functions, which is used as a key element in our demonstrations along with several basic inequalities such as: power mean inequality, and Holder’s inequality. The symmetry of the Hermite-Hadamard type inequalities is stressed by the different types of convexities. Several special cases of the parameter are chosen to illustrate the investigated results. Four examples are presented.

Keywords

• q-calculus
• convexity
• midpoint inequalities
• Hermite-Hadamard type inequalities