Extension of Stolarsky means by Euler-Radau expansions

Abstract

We present construction of exponentially convex functions via functionals that follow from some inequalities for convex functions. These inequalities are derived from expansions of Euler and Radau. Using fruitful properties of exponential convexity we construct various means that have nice monotone properties over defining parameters. We further show how known results about Cauchy means can be treated in a succinct way.