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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Stability problem for number-theoretically multiplicative functions


Authors: Tomasz Kochanek and Michal Lewicki
Journal: Proc. Amer. Math. Soc. 135 (2007), 2591-2597
MSC (2000): Primary 39B82
DOI: https://doi.org/10.1090/S0002-9939-07-08854-5
Published electronically: February 9, 2007
MathSciNet review: 2302580
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Abstract | References | Similar Articles | Additional Information

Abstract: We deal with the stability question for multiplicative mappings in the sense of number theory. It turns out that the conditional stability assumption:

$\displaystyle \vert f(xy)-f(x)f(y)\vert\leq\varepsilon$   for relatively prime $\displaystyle x,y$

implies that $ f$ lies near to some number-theoretically multiplicative function. The domain of $ f$ can be general enough to admit, in special cases, the reduction of our result to the well known J. A. Baker - J. Lawrence - F. Zorzitto superstability theorem.


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Additional Information

Tomasz Kochanek
Affiliation: Institute of Mathematics, Silesian University, Bankowa 14, PL-40 007 Katowice, Poland
Email: t_kochanek@wp.pl

Michal Lewicki
Affiliation: Institute of Mathematics, Silesian University, Bankowa 14, PL-40 007 Katowice, Poland
Email: m_lewicki@wp.pl

DOI: https://doi.org/10.1090/S0002-9939-07-08854-5
Keywords: Conditional functional equation, stability, arithmetic functions
Received by editor(s): May 1, 2006
Published electronically: February 9, 2007
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.