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Abstract. We study necessary and sufficient conditions on linear operators A and B for inequality A f B f to hold for every function f that is n -convex at a point.Mathematics subject classification (2010): 26D99, 26D15.

Abstract. In this paper, we extend some Hardy-type inequalities with certain kernels to arbitrary time scales. Certain classical and some new integral and discrete inequalities are deduced in seek of applications.Mathematics subject classification (2010): 26D15, 34N05, 28A25.

In this note it is proved that the integral arithmetic mean of a convex function is a Schur-convex function. Applications to Schur-convexity of logarithmic mean and gamma functions are given.

Abstract. We give a generalization of Steffensen's inequality by extending the results of Pečarić [4] and Rabier [5]. We make use of the n -order Taylor expansion of a composition of functions and Faà di Bruno's formula for higher order derivatives of the composition.Mathematics subject classification (2010): 26D10, 26D15.