Back to Search
Start Over
Remarks on a paper about functional inequalities for polynomials and Bernoulli numbers
- Source :
- Aequationes mathematicae. 78:177-183
- Publication Year :
- 2009
- Publisher :
- Springer Science and Business Media LLC, 2009.
-
Abstract
- 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.
Details
- ISSN :
- 14208903 and 00019054
- Volume :
- 78
- Database :
- OpenAIRE
- Journal :
- Aequationes mathematicae
- Accession number :
- edsair.doi...........c266d59d141eb68acdb9e2f6be45d72c