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.
Highlights
The logarithmic mean L(a, b) of two positive numbers a and b is defined by L(a, b) = log a−b a−log b, a = b, a, a = b. (1:1)Recently, the logarithmic mean has been: the subject of intensive research
Many remarkable inequalities for the logarithmic mean can be found in the literature [1-30]
It might be surprising that the logarithmic mean has applications in physics, economics, and even in meteorology [31-33]
Summary
1 Introduction The logarithmic mean L(a, b) of two positive numbers a and b is defined by The logarithmic mean has been: the subject of intensive research. Many remarkable inequalities for the logarithmic mean can be found in the literature [1-30]. It might be surprising that the logarithmic mean has applications in physics, economics, and even in meteorology [31-33].
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