Comparison of differences between arithmetic and geometric means

2010/01/27 by J. M. Aldaz, Aldaz, J. M.
Mathematics · #26D15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26D15

paper · pdf · doi:10.48550/arxiv.1001.5055

Improvements on the bounds after becoming aware of the paper by Sever S. Dragomir, "Bounds for the normalised Jensen functional", Bull. Austral. Math. Soc. 74 (2006), no. 3, 471--478. Correction of an error and of some typos

arxiv created 2010/10/07 · arxiv updated 2010/10/08

Abstract

We complement a recent result of S. Furuichi, by showing that the differences ∑_i=1ⁿ α_i x_i - ∏_i=1ⁿ x_i^α_i associated to distinct sequences of weights are comparable, with constants that depend on the smallest and largest quotients of the weights.

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