Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some New Inequalities Between Important Means   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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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph