Bounds for the Neuman–Sándor Mean in Terms of the Arithmetic and Contra-Harmonic Means

Bounds for the Neuman–Sándor Mean in Terms of the Arithmetic and Contra-Harmonic Means

In this paper, the authors provide several sharp upper and lower bounds for the Neuman–Sándor mean in terms of the arithmetic and contra-harmonic means, and present some new sharp inequalities involving hyperbolic sine function and hyperbolic cosine function.

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Veröffentlicht in:Axioms 2022-05, Vol.11 (5), p.236
Hauptverfasser: Li, Wen-Hui, Miao, Peng, Guo, Bai-Ni
Format: Artikel
Sprache:eng
Schlagworte:
Arithmetic
arithmetic mean
bound
contra-harmonic mean
Hyperbolic functions
hyperbolic sine function
Inequality
Lower bounds
Neuman–Sándor mean
Trigonometric functions
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Beschreibung
Zusammenfassung:In this paper, the authors provide several sharp upper and lower bounds for the Neuman–Sándor mean in terms of the arithmetic and contra-harmonic means, and present some new sharp inequalities involving hyperbolic sine function and hyperbolic cosine function.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11050236