Several Quantum Hermite–Hadamard-Type Integral Inequalities for Convex Functions

Abstract

The aim of this study was to present several improved quantum Hermite–Hadamard-type integral inequalities for convex functions using a parameter. Thus, a new quantum identity is proven to be used as the main tool in the proof of our results. Consequently, in some special cases several new quantum estimations for q-midpoints and q-trapezoidal-type inequalities are derived with an example. The results obtained could be applied in the optimization of several economic geology problems.

Keywords

• quantum calculus
• convex functions
• Hermite–Hadamard-type inequalities