A Review of Hermite–Hadamard Inequality for <i>α</i>-Type Real-Valued Convex Functions

Abstract

Inequalities play important roles not only in mathematics but also in other fields, such as economics and engineering. Even though many results are published as Hermite–Hadamard (H-H)-type inequalities, new researchers to these fields often find it difficult to understand them. Thus, some important discoverers, such as the formulations of H-H-type inequalities of α-type real-valued convex functions, along with various classes of convexity through differentiable mappings and for fractional integrals, are presented. Some well-known examples from the previous literature are used as illustrations. In the many above-mentioned inequalities, the symmetrical behavior arises spontaneously.

Keywords

• convex functions
• generalized convex functions
• fractional integrals
• Hermite–Hadamard inequality