New Inequalities of Hermite-hadamard Type for Functions Whose Second Derivatives Absolute Values Are Quasi-convex

hold. This double inequality is known in the literature as the Hermite–Hadamard inequality for convex functions. In recent years many authors established several inequalities connected to this fact. For recent results, refinements, counterparts, generalizations and new Hermite-Hadamard’stype inequalities see [1]–[18]. We recall that the notion of quasi-convex function generalizes the notion of convex function. More exactly, a function f : [a, b] → R is said to be quasi-convex on [a, b] if f (λx+ (1− λ) y) ≤ max {f (x) , f (y)} , ∀x, y ∈ [a, b] . (1.1)