A modification of an elementary numerical inequality

Krassimir Atanassov
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 18, 2012, Number 3, Pages 5–7
Full paper (PDF, 109 Kb)

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Authors and affiliations

Krassimir Atanassov
Dept. of Bioinformatics and Mathematical Modelling
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria

Abstract

It is proved that for every real numbers a_{0}, a_{1}, ... , a_{n} (n \geq 1):

    \[\sum^{n-1}_{k=0} a_{k+1}.(a_{k} - a_{k+1}) \leq \fral{1}{2.n}.\sum^{n-1}_{k=0} a_{k}^2.\]

This is a modification of an inequality, previously introduced by the author.

Keywords

  • Arithmetic functions
  • Inequalities

AMS Classification

  • 11A25

References

  1. Atanassov, K., An elementary numerical inequality. The Australian Mathematical Society Journal, Vol. 24, 1997, No. 5, 182
  2. Beran, L., E. Novakova, On an inequality of Atanassov. The Australian Mathematical Society Journal, Vol. 25, 1998, No. 5, 234–235.
  3. Coope, I., P. Renaud, A quadratic inequality of Atanassov. The Australian Mathematical Society Journal, Vol. 26, 1999, No. 4, 169–170.

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Cite this paper

Atanassov, K. (2012). A modification of an elementary numerical inequality. Notes on Number Theory and Discrete Mathematics, 18(3), 5-7.

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