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Proceedings of the American Mathematical Society

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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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0633285-6
Keywords: Functional equation, stability
Article copyright: © Copyright 1982 American Mathematical Society