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 0022-247XFull text not available from this repository.
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.
|Journal or Publication Title:||Journal of Mathematical Analysis and Applications|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||18 Nov 2008 11:46|
|Last Modified:||26 Jul 2012 15:28|
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