Some New Inequalities Between Important Means

Details Some New Inequalities Between Important Means Some New Inequalities Between Important Means

2007-10-19

arxiv.org/abs/0710.3681v1

Mathematical Inequalities & Applications (MIA), Volume 10, Number 3 (2007), 517-527

Mathematics

Classical Analysis and ODEs

Selected paper in 14th Seminar on Mathematical Analysis and its Applications, February 4-5, 2004, Iran University of Science a

Scientific paper

In this paper, mainly using the convexity of the function $\frac{a^x-b^x}{c^x-d^x}$ and convexity or concavity of the function $\ln\frac{a^x-b^x}{c^x-d^x}$ on the real line, where $a>b\geq c>d>0$ are fixed real numbers, we obtain some important relations between various important means of these numbers. Also, we apply the obtained results to Ky Fan type inequalities and get some new refinements.

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