Some inequalities for functions having Orlicz-convexity

Some Hermite–Hadamard type inequalities are derived for products of functions having Orlicz-convexity properties. We also obtain these inequalities via Riemann–Liouville fractional integrals for Orlicz-convex functions. These inequalities are as best as possible from the sharpness point of view, meaning that a sharpness class of functions is identified, for each inequality, within the functions that are s-affine of first kind. Some special cases are discussed.