Some Elementary Aspects of Means

Abstract EN

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.