Arithmetic mean of values and value at mean of arguments for convex functions

Abstract

We give here some extensions of inequalities of T. Popoviciu and T. Rado. The idea is to use an inequality ([2], p.4) which gives an approximation of the arithmetic mean of n values of a given convex function in terms of the value at the arithmetic mean of the arguments. We also give more general forms of this inequality by replacing the arithmetic mean with others. Finally we use these inequalities to establish similar inequalities of T. Popoviciu and T. Rado type. doi:10.1017/S1446181108000199