Copyright c © 2014 J. Jakšetic ́ et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract. We present construction of exponentially convex functions via functionals that follow from some in-equalities 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 definin
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