On the Arithmetic-Geometric-Harmonic-Mean Inequalities

Mohammad Al-Hawari; Ayat Almomani; Mohammad A. Bani Abdelrahman

doi:10.5269/bspm.80385

Mohammad Al-Hawari Ajloun National University
Ayat Almomani
Mohammad A. Bani Abdelrahman

Abstract

In this article, we collect some inequalities concerning, Arithmetic, Geometric, Young and Heinz inequalities, the goal of the thesis is to investigate Young and Heinz inequalities for scalars and matrices. Improvements to the inequality studied of arithmetic and geometric means for scalars and several other auxiliary results; we provided some improvements to the inequality of arithmetic and geometric means by using the convex functions. A fundamental relationship between positive real numbers and the v-weighted arithmetic-geometric mean inequality is presented for any two scalars. Also, we introduce the largest and the smallest eigenvalues inequalities for matrices by using our subjects.

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References

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