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for all x 2 [a; b]. The constant 1 4 is the best possible. This inequality is well known in the literature as the Ostrowski inequality. Denition 1. The function f : [a; b] R! R, is said to be convex if the following inequality holds f(tx+ (1 t)y) tf(x) + (1 t)f(y) for all x; y 2 [a; b] and t 2 [0; 1] : We say that f is concave if ( f) is convex. Let f : I R !R be a convex function on the interval I of real numbers and a; b 2 I with a < b. If f is a convex function then the following double inequality, which is well known in the literature as the HermiteHadamard inequality, holds [13]

On generalized Ostrowski-type inequalities for functions whose first derivatives absolute values are convex