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Monotonic averages of convex functions.

Bennet, Grahame and Jameson, Graham J. O. (2000) Monotonic averages of convex functions. Journal of Mathematical Analysis and Applications, 252 (1). pp. 410-430. ISSN 0022-247X

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Abstract

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.

Item Type: Article
Journal or Publication Title: Journal of Mathematical Analysis and Applications
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19328
Deposited By: ep_ss_importer
Deposited On: 18 Nov 2008 11:46
Refereed?: Yes
Published?: Published
Last Modified: 14 Oct 2013 12:55
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19328

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