We consider inequalities which incorporate both Jensen and Ostrowski type inequalities for functions with absolutely continuous n-th derivative. We provide applications of these inequalities for divergence measures. In particular, we obtain inequalities involving higher order χ-divergence.

Using a variant of Grüss inequality, to give a new proof of a well known result on Ostrowski-Grüss type inequalities and sharpness of this inequality is obtained. Moreover, a new general sharp Ostrowski-Grüss type inequality is given.

Some inequalities of Ostrowski type for isotonic linear functionals defined on a linear class of function L := {f : [a, b] → R} are established. Applications for integral and discrete inequalities are also given.

A theorem of A. Ostrowski describing meromorphic functions f such that the family {f(λz) : λ ∈ C∗} is normal, is generalized to holomorphic maps from C∗ to a projective space. MSC 2010: 30D45, 32A19.