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International Journal of Mathematics and Mathematical Sciences
Volume 2013, Article ID 689560, 9 pages
http://dx.doi.org/10.1155/2013/689560
Research Article

Some Elementary Aspects of Means

Department of Mathematics, Yarmouk University, Irbid, Jordan

Received 24 December 2012; Accepted 31 March 2013

Academic Editor: Peter Bullen

Copyright © 2013 Mowaffaq Hajja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We raise several elementary questions pertaining to various aspects of means. These questions refer to both known and newly introduced families of means, and include questions of characterizations of certain families, relations among certain families, comparability among the members of certain families, and concordance of certain sequences of means. They also include questions about internality tests for certain mean-looking functions and about certain triangle centers viewed as means of the vertices. The questions are accessible to people with no background in means, and it is also expected that these people can seriously investigate, and contribute to the solutions of, these problems. The solutions are expected to require no more than simple tools from analysis, algebra, functional equations, and geometry.