Monotonic averages of convex functions
type: Item
instance of: scholarly article
title: Monotonic averages of convex functions
zbMATH Open document ID: 0972.26007
author: Grahame Bennett
author: G. J. O. Jameson
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-02-11T00:00:00Z
review text: This very nice paper contains several interesting results. The authors summarize its subject as follows: ``We investigate the monotonicity of various averages of the values of a convex (or concave) function at \(n\) equally spaced points. For a convex function, averages without end points increase with \(n\), while averages with end points decrease. Averages including one end point are treated as a special case of upper and lower Riemann sums, which are shown to decrease and increase, respectively. Corresponding results for mid-point Riemann sums and the trapezium estimate require convexity or concavity of the derivative as well as the function. Special cases include some known results and some new ones, unifying them in a more systematic theory. Further applications include results on series and power majorization''.
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 1563469
zbMATH Keywords: averages
zbMATH Keywords: end points
zbMATH Keywords: Riemann sums
zbMATH Keywords: convexity
zbMATH Keywords: concavity
reviewed by: László Leindler
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7087
OpenAlex ID: W2061934099
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DOI: 10.1006/JMAA.2000.7087
description: scientific article; zbMATH DE number 1563469