aequationes mathematicae

, Volume 31, Issue 1, pp 243–246 | Cite as

The octahedron equation implies the cube equation: An elementary proof

  • J. A. MacDougall
  • K. Ozeki
Research Papers

Abstract

It has been proved by L. Sweet that the “octahedron” functional equation implies the “cube” functional equation in all dimensionsn≧1. In this note we give an elementary proof of this theorem.

AMS (1980) subject classification

Primary 39B40 

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Reference

  1. [1]
    Sweet, L.,On the generalized cube and octahedron functional equations. Aequationes Math.22 (1981), 29–38.Google Scholar

Copyright information

© Birkhäuser Verlag 1986

Authors and Affiliations

  • J. A. MacDougall
    • 1
    • 2
  • K. Ozeki
    • 1
    • 2
  1. 1.Dept. of Mathematics and Computer ScienceUniversity of Prince Edward IslandCharlottetownCanada
  2. 2.Department of Mathematics, Faculty of General EducationUtsunomiya UniversityUtsunomiyaJapan

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