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Mathematical Notes

, Volume 103, Issue 1–2, pp 209–220 | Cite as

A Logarithmic Inequality

  • G. V. Kalachev
  • S. Yu. Sadov
Article
  • 23 Downloads

Abstract

The inequality
$$\ln {\kern 1pt} \ln \left( {r - \ln r} \right) + 1 < \mathop {\min }\limits_{0 < x \leqslant r - 1} \left( {\ln x + {x^{ - 1}}\ln \left( {r - x} \right)} \right) < \ln {\kern 1pt} \ln \left( {r - \ln \left( {r - {2^{ - 1}}\ln r} \right)} \right) + 1,$$
where r > 2, is proved. A combinatorial optimization problem which involves the function to be minimized is described.

Keywords

logarithmic inequality two-sided estimate extremal graph 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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