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Aequationes mathematicae

, 78:177 | Cite as

Remarks on a paper about functional inequalities for polynomials and Bernoulli numbers

  • Jens Schwaiger
Article
  • 40 Downloads

Summary.

The authors of [KMM] consider a system of two functional inequalities for a function \(f : {\mathbb{R}} \rightarrow {\mathbb{R}}\), and they show that, if certain arithmetical conditions and inequalities for certain parameters are fulfilled, f has to be a polynomial provided that f is continuous at some point x0. This result is derived here under the weaker condition that for some x0 the limit \({\rm lim}_{x \rightarrow x_0} f(x)\) exists. Moreover, another system of inequalities is given leading to the same result on the nature of f. The methods used also give natural explanations for the fact that Bernoulli numbers play an important role in this context.

Mathematics Subject Classification (2000).

Primary 39B72, 26D16 secondary 11B68, 11B83 

Keywords.

Functional inequalities difference equations polynomials polynomial sequences 

Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.Institut für MathematikUniversität GrazGrazÖsterreich

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