Extension of a generalized Pexider equation

Author:
János Aczél

Journal:
Proc. Amer. Math. Soc. **133** (2005), 3227-3233

MSC (2000):
Primary 39B22

Published electronically:
June 20, 2005

MathSciNet review:
2161144

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Abstract: The equations and , called Pexider equations, have been completely solved on If they are assumed to hold only on an open region, they can be extended to (the second when is nowhere 0) and solved that way. In this paper their common generalization is extended from an open region to and then completely solved if is not constant on any proper interval. This equation has further interesting particular cases, such as and that arose in characterization of geometric and power means and in a problem of equivalence of certain utility representations, respectively, where the equations may hold only on an open region in Thus these problems are solved too.

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Additional Information

**János Aczél**

Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Email:
jdaczel@math.uwaterloo.ca

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08039-1

Keywords:
Functional equations,
extensions,
generalized Pexider equation

Received by editor(s):
February 25, 2004

Published electronically:
June 20, 2005

Additional Notes:
This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada grant OGP 0002972. The author is grateful for an observation by Fulvia Skof.

Communicated by:
M. Gregory Forest

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.