Note On Certain Inequalities for Neuman Means
Zai-Yin He, Yu-Ming Chu, Ying-Qing Song, Xiao-Jing Tao
TL;DR
This paper derives explicit formulas for Neuman means and establishes optimal bounds for these means using harmonic, arithmetic, and contraharmonic means, enhancing understanding of their inequalities.
Contribution
It provides explicit formulas for Neuman means and determines the best possible bounds in terms of harmonic, arithmetic, and contraharmonic means.
Findings
Explicit formulas for Neuman means $N_{AH}$, $N_{HA}$, $N_{AC}$, $N_{CA}$
Optimal upper and lower bounds for Neuman means
Enhanced understanding of inequalities among means
Abstract
In this paper, we give the explicit formulas for the Neuman means , , and , and present the best possible upper and lower bounds for theses means in terms of the combinations of harmonic mean , arithmetic mean and contraharmonic mean .
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Taxonomy
TopicsMathematical Inequalities and Applications · Functional Equations Stability Results · Analytic and geometric function theory