Abstract
The aim of this paper is two-fold: First we describe a certain class of strictly positive, continuous functions u:I→ℝ defined on certain intervals I⊂]0,+∞[, and demonstrate that each function u of this class permits the definition of an associated mean Mu (a1,...,an) for any finite number a1,...,an of numbers in I. The arithmetic and the geometric mean are special cases of these u-means Mu. -Thereafter, we improve the classical inequality between the geometric and the arithmetic mean and derive from it a corresponding inequality between certain u-means and the arithmetic mean.
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Bauer, H. A class of means and related inequalities. Manuscripta Math 55, 199–211 (1986). https://doi.org/10.1007/BF01168685
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DOI: https://doi.org/10.1007/BF01168685