Geodesic
A Logarithmic Inequality
Matematičeskie zametki, Tome 103 (2018) no. 2, pp. 210-222.

Voir la notice de l'article provenant de la source Math-Net.Ru

The inequality \begin{equation*} \ln\ln(r-\ln r)+1 \min_{0\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. 
@article{MZM_2018_103_2_a4,
     author = {G. V. Kalachev and S. Yu. Sadov},
     title = {A {Logarithmic} {Inequality}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {210--222},
     publisher = {mathdoc},
     volume = {103},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_2_a4/}
}
TY  - JOUR
AU  - G. V. Kalachev
AU  - S. Yu. Sadov
TI  - A Logarithmic Inequality
JO  - Matematičeskie zametki
PY  - 2018
SP  - 210
EP  - 222
VL  - 103
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_2_a4/
LA  - ru
ID  - MZM_2018_103_2_a4
ER  - 
%0 Journal Article
%A G. V. Kalachev
%A S. Yu. Sadov
%T A Logarithmic Inequality
%J Matematičeskie zametki
%D 2018
%P 210-222
%V 103
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_2_a4/
%G ru
%F MZM_2018_103_2_a4
G. V. Kalachev; S. Yu. Sadov. A Logarithmic Inequality. Matematičeskie zametki, Tome 103 (2018) no. 2, pp. 210-222. http://geodesic.mathdoc.fr/item/MZM_2018_103_2_a4/

[1] H. Robbins, “A remark on Stirling's formula”, Amer. Math. Monthly, 62:1 (1955), 26–29 | DOI | MR | Zbl

[2] N. Batir, “Sharp inequalities for factorial $n$”, Proyecciones, 27:1 (2008), 97–102 | DOI | MR | Zbl

[3] N. Batir, M. Cancan, “Sharp inequalities involving the constant $e$ and the sequence $(1+1/n)^n$”, Internat. J. Math. Ed. Sci. Tech., 40:8 (2009), 1101–1109 | DOI | MR | Zbl

[4] B. Akbarpour, L. C. Paulson, “MetiTarski: an automatic theorem prover for real-valued special functions”, J. Automat. Reason., 44:3 (2010), 175–205 | DOI | MR | Zbl

[5] A. S. Podkolzin, Kompyuternoe modelirovanie logicheskikh protsessov. T. 3. Opyt obucheniya reshatelya zadach: matematicheskii analiz, differentsialnye uravneniya i elementarnaya geometriya, MGU, M., 2015 http://intsys.msu.ru/staff/podkolzin/tom3.pdf

[6] J. Sándor, “A note on inequalities for the logarithmic function”, Octogon Math. Magazine, 17:1 (2009), 299–301

[7] F. Topsøe, “Some bounds for the logarithmic function”, Inequality Theory and Applications, V. 4, Nova Sci. Publ., New York, 2007, 137–151 | MR

[8] R. Stenli, Perechislitelnaya kombinatorika, T. 1, Mir, M., 1990 | MR