We introduce a class of h-convex functions which generalize convex, s-convex, Godunova-Levin functions and P -functions. Namely, the h-convex function is defined as a non-negative function f :where h is a non-negative function, α ∈ (0, 1) and x, y ∈ J . Some properties of h-convex functions are discussed. Also, the Schur-type inequality is given.

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Abstract. We provide generalizations and improvements of a variety of recent results for the Ostrowski and Simpson inequalities.Mathematics subject classification (1991): 26D10.

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Abstract. We obtain integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality.Mathematics subject classification (2010): 26D15, 34N05, 28A25.