New versions of the Hermite–Hadamard inequality for ( ϕ − h ) $(\phi -h)$ -integrals

Abstract

Abstract In this paper, we prove some new versions of the Hermite–Hadamard inequality for ( ϕ − h ) $({\phi}-h)$ -integrals. For this aim, we use the tangent and secant lines at the same special points. Moreover, we investigate the relations between the newly obtained results and earlier published papers. We also present some new results by special choices of ϕ and h.

Keywords

• ( ϕ − h ) $({\phi}-h)$ -derivative
• ( ϕ − h ) $({\phi}-h)$ -integral
• Convex function
• Hermite–Hadamard Inequality