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International Journal of Mathematics Trends and Technology

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Volume 69 | Issue 5 | Year 2023 | Article Id. IJMTT-V69I5P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I5P507

On a Mixed Arithmetic-Mean, Geometric-Mean, Harmonic-Mean Inequality


Kyumin Nam
Received Revised Accepted Published
01 Apr 2023 05 May 2023 16 May 2023 31 May 2023
Abstract

In 1992, F. Holland [1] conjectured the following mixed arithmetic-mean, geometric-mean inequality:

                                                                                                        

Where x1, x2, …, xn are positive real numbers with equality if and only if x1 = x2 = … = xn. And K. Kedlaya [2] proved it in 1994. We can extend this inequality, and the purpose of this paper is to address it. 

Keywords
Arithmetic mean, Geometric mean, Harmonic mean, Mixed mean, Mixed mean inequality.
References

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Citation :

Kyumin Nam, "On a Mixed Arithmetic-Mean, Geometric-Mean, Harmonic-Mean Inequality," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 5, pp. 78-81, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I5P507

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