On Generalized Means

Authors

H. P. Thielman, Iowa State CollegeFollow

Document Type

Research

Abstract

Every student of elementary mathematics is acquainted with the concepts of the arithmetic mean, the harmonic mean, and the geometric mean of sets of numbers. These concepts are also common mathematical tools used in the analysis of data in many applied sciences. It may not be so well known that there exist various types of means of which those mentioned above are very special cases. It is the object of this paper to give postulational definitions of the concept of means in general, and to derive certain relations between different kinds of means. In this connection it will also be shown that certain classes of functions, namely convex functions, can be defined in terms of the notion of means.

Publication Date

1949

Journal Title

Proceedings of the Iowa Academy of Science

Volume

56

Issue

1

First Page

241

Last Page

247

Copyright

©1949 Iowa Academy of Science, Inc.

Language

en

File Format

application/pdf

Recommended Citation

Thielman, H. P. (1949) "On Generalized Means," Proceedings of the Iowa Academy of Science, 56(1), 241-247.
Available at: https://scholarworks.uni.edu/pias/vol56/iss1/33