The stability of the exponential equation
Authors:
Roman Ger and Peter Semrl
Journal:
Proc. Amer. Math. Soc. 124 (1996), 779787
MSC (1991):
Primary 39B72
MathSciNet review:
1291769
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Abstract: We generalize the wellknown Baker's superstability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary commutative complex semisimple Banach algebra. It was shown by Ger that the superstability phenomenon disappears if we formulate the stability question for exponential complexvalued functions in a more natural way. We improve his result by showing that the maximal possible distance of an approximately exponential function to the set of all exponential functions tends to zero as tends to zero. In order to get this result we have to prove a stability theorem for realvalued functions additive modulo the set of all integers .
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Additional Information
Roman Ger
Affiliation:
Institute of Mathematics, Silesian University, Bankowa 14, 40007 Katowice, Poland
Peter Semrl
Affiliation:
TF, University of Maribor, Smetanova 17, P.O. BOX 224, 62000 Maribor, Slovenia
DOI:
http://dx.doi.org/10.1090/S0002993996030316
PII:
S 00029939(96)030316
Keywords:
Exponential functions,
congruentialy additive functions,
stability
Received by editor(s):
February 1, 1994
Received by editor(s) in revised form:
July 24, 1994
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1996
American Mathematical Society
