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2012•Journal of Inequalities and ApplicationsOpen access

Optimal generalized Heronian mean bounds for the logarithmic mean

Hongxing Shi, Bo-Yong Long, Yu‐Ming Chu

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Abstract

Abstract In this article, we establish a double inequality between the generalized Heronian and logarithmic means. The achieved result is inspired by the articles of Lin and Shi et al., and the methods from Janous. The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. 2010 Mathematics Subject Classification:26E60.

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Abstract In this article, we establish a double inequality between the generalized Heronian and logarithmic means. The achieved result is inspired by the articles of Lin and Shi et al., and the methods from Janous. The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. 2010 Mathematics Subject Classification:26E60.

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Available abstract

Abstract In this article, we establish a double inequality between the generalized Heronian and logarithmic means. The achieved result is inspired by the articles of Lin and Shi et al., and the methods from Janous. The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. 2010 Mathematics Subject Classification:26E60.

Key concepts: Mathematics, Logarithm, Logarithmic mean, Mathematics Subject Classification, Inequality, Subject (documents), Combinatorics, Pure mathematics

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