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Linked pairs of additive functions.
- Source :
- Aequationes Mathematicae; Dec2017, Vol. 91 Issue 6, p1025-1040, 16p
- Publication Year :
- 2017
-
Abstract
- In 1990, Benz asked whether a real additive mapping satisfying $$xf(y)=yf(x)$$ for all points ( x, y) on the unit circle must be linear. In 2005, Boros and Erdei showed that it must be so. Here we generalize the problem to a pair of additive functions f, g related by the functional equation $$xf(y)=yg(x)$$ for all points ( x, y) on a specified curve. We find that for many (but not all) types of curves this forces f and g to be equal and linear. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 91
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 126542202
- Full Text :
- https://doi.org/10.1007/s00010-017-0514-7