Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals

Abstract

Abstract In this paper, we introduce ( h 1 , h 2 ) $(h_{1},h_{2})$ -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.

Keywords

• Invex sets
• Preinvex functions
• Interval-valued functions
• Hermite–Hadamard inequalities
• Fractional integrals