On a theorem of Baker, Lawrence and Zorzitto
Author:
L. Székelyhidi
Journal:
Proc. Amer. Math. Soc. 84 (1982), 95-96
MSC:
Primary 39B50
DOI:
https://doi.org/10.1090/S0002-9939-1982-0633285-6
MathSciNet review:
633285
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The result of J. Baker, J. Lawrence and F. Zorzitto on the stability of the equation $f(x + y) = f(x)f(y)$ is generalized by proving the following theorem: if $G$ is a semigroup and $V$ is a right invariant linear space of complex valued functions on $G$, and if $f$, $m$ are complex valued functions on $G$ for which the function $x \to f(xy) - f(x)m(y)$ belongs to $V$ for every $y$ in $G$, then either $f$ is in $V$ or $m$ is exponential.
- John Baker, J. Lawrence, and F. Zorzitto, The stability of the equation $f(x+y)=f(x)f(y)$, Proc. Amer. Math. Soc. 74 (1979), no. 2, 242–246. MR 524294, DOI https://doi.org/10.1090/S0002-9939-1979-0524294-6
- John A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 411–416. MR 580995, DOI https://doi.org/10.1090/S0002-9939-1980-0580995-3
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 39B50
Retrieve articles in all journals with MSC: 39B50
Additional Information
Keywords:
Functional equation,
stability
Article copyright:
© Copyright 1982
American Mathematical Society