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Problemy Analiza — Issues of Analysis, 2017, Volume 6(24), Issue 1, Pages 46–57
DOI: https://doi.org/10.15393/j3.art.2017.3770 (Mi pa215) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Wilker and Huygens-type inequalities involving Gudermannian and the inverse Gudermannian functions

E. Neuman

Mathematical Research Institute, 144 Hawthorn Hollow, Carbondale IL 62903, USA
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DOI: https://doi.org/10.15393/j3.art.2017.3770
Abstract: Five Wilker Huygens-type inequalities involving Gudermannian and the inverse Gudermannian functions are obtained. The Schwab–Borchardt mean plays a crucial role in the proofs. Also, an analytical inequality for the sums of powers, established earlier by this author, is an indispensable tool in the the proofs of the main results of this paper.
Keywords: Gudermannian function, inverse Gudermannian function, Wilker inequality, Schwab–Borchardt mean, Huygens inequality, inequalities.
Received: 11.04.2017
Revised: 06.06.2017
Accepted: 06.06.2017
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: 26D07, 26E60
Language: English
Citation: E. Neuman, “Wilker and Huygens-type inequalities involving Gudermannian and the inverse Gudermannian functions”, Probl. Anal. Issues Anal., 6(24):1 (2017), 46–57
Citation in format AMSBIB
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\by E.~Neuman
\paper Wilker and Huygens-type inequalities involving Gudermannian and the inverse Gudermannian functions
\jour Probl. Anal. Issues Anal.
\yr 2017
\vol 6(24)
\issue 1
\pages 46--57
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\crossref{https://doi.org/10.15393/j3.art.2017.3770}
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    		Problemy Analiza — Issues of Analysis
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