On a new class of convex functions and integral inequalities

Abstract

Abstract The aim of this paper is to introduce a new extension of convexity called σ-convexity. We show that the class of σ-convex functions includes several other classes of convex functions. Some new integral inequalities of Hermite–Hadamard type are established to illustrate the applications of σ-convex functions.

Keywords

• Convex functions
• σ-convex functions
• Hermite–Hadamard inequality
• Integral inequalities