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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Stability problem for number-theoretically multiplicative functions
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by Tomasz Kochanek and Michał Lewicki PDF
Proc. Amer. Math. Soc. 135 (2007), 2591-2597 Request permission

Abstract:

We deal with the stability question for multiplicative mappings in the sense of number theory. It turns out that the conditional stability assumption: \[ |f(xy)-f(x)f(y)|\leq \varepsilon \;\text {for relatively prime $x$, $y$} \] 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
  • MR Author ID: 811694
  • Email: t_kochanek@wp.pl
  • Michał Lewicki
  • Affiliation: Institute of Mathematics, Silesian University, Bankowa 14, PL-40 007 Katowice, Poland
  • Email: m_lewicki@wp.pl
  • Received by editor(s): May 1, 2006
  • Published electronically: February 9, 2007
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2591-2597
  • MSC (2000): Primary 39B82
  • DOI: https://doi.org/10.1090/S0002-9939-07-08854-5
  • MathSciNet review: 2302580