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Log-concavity
of Hölder means and an application to geometric
inequalities
Aurel I. Stan and Sergio D. Zapeta-Tzul
Vol. 12 (2019), No. 4, 671–686
DOI: 10.2140/involve.2019.12.671
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Abstract |
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The log-concavity of the Hölder mean of two numbers, as a function of its index, is presented first. The notion of -cevian of a triangle is introduced next, for any real number . We use this property of the Hölder mean to find the smallest index such that the length of an -cevian of a triangle is less than or equal to the -Hölder mean of the lengths of the two sides of the triangle that are adjacent to that cevian. |
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Keywords
Hölder mean, log-concavity, Jensen inequality, triangle,
cevian
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Mathematical Subject Classification 2010
Primary: 26A06, 26D99
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Milestones
Received: 23 May 2018
Revised: 9 November 2018
Accepted: 15 November 2018
Published: 16 April 2019
Communicated by Sever S. Dragomir
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Authors |
| Aurel I. Stan | |
| Department of Mathematics Ohio State University at Marion Marion, OH United States |
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| Sergio D. Zapeta-Tzul | |
| Department of Mathematics Universidad del Valle de Guatemala Guatemala Guatemala |
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