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Mat. Zametki, 2018, Volume 103, Issue 2, Pages 210–222 (Mi mz11556)  

A Logarithmic Inequality

G. V. Kalacheva, S. Yu. Sadov

a Lomonosov Moscow State University

Abstract: The inequality
\begin{equation*} \ln\ln(r-\ln r)+1 <\min_{0<x\le r-1} (\ln x+ x^{-1}\ln(r-x)) <\ln\ln(r-\ln(r-2^{-1}\ln r))+1, \end{equation*}
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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11556

Full text: PDF file (579 kB)
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English version:
Mathematical Notes, 2018, 103:2, 209–220

Bibliographic databases:

UDC: 517.272+519.176
Received: 12.02.2017
Revised: 23.04.2017

Citation: G. V. Kalachev, S. Yu. Sadov, “A Logarithmic Inequality”, Mat. Zametki, 103:2 (2018), 210–222; Math. Notes, 103:2 (2018), 209–220

Citation in format AMSBIB
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