On Hermite–Hadamard–Fejér-Type Inequalities for <i>η</i>-Convex Functions via Quantum Calculus

Abstract

In this paper, we use qa- and qb-integrals to establish some quantum Hermite–Hadamard–Fejér-type inequalities for η-convex functions. By taking q→1, our results reduce to classical results on Hermite–Hadamard–Fejér-type inequalities for η-convex functions. Moreover, we give some examples for quantum Hermite–Hadamard–Fejér-type inequalities for η-convex functions. Some results presented here for η-convex functions provide extensions of others given in earlier works for convex and η-convex functions.

Keywords

• Hermite–Hadamard–Fejér-type integral inequalities
• <i>η</i>-convex function
• quantum calculus
• <i>q_a</i>-integral
• <i>q^b</i>-integral