Wilker-Huygens Inequalities Involving Generalized Trigonometric and Hyperbolic Function

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On Some Inequalities Involving Trigonometric and Hyperbolic Functions with Emphasis on the Cusa–huygens, Wilker, and Huygens Inequalities

Recently trigonometric inequalities of N. Cusa and C. Huygens (see, e.g., [9]), J. Wilker [11], and C. Huygens [4] have been discussed extensively in mathematical literature. We shall demonstrate that Wilker’s inequality, Huygens’ inequality, and some other related inequalities all follow from the Cusa-Huygens inequality. A generalization of the latter result is also obtained. The hyperbolic co...

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Inequalities involving generalized trigonometric and hyperbolic functions

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Inequalities Involving Hyperbolic Functions and Trigonometric Functions

Inequalities involving hyperbolic functions and trigonometric functions are established. Most of the established inequalities can be regarded as the companion inequalities to those obtained by Lazarević, Adamović and Mitrinović and Cusa and Huygens The established results are obtained with the aid of the Schwab-Borchardt mean.

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On Wilker and Huygens Type Inequalities

Trigonometric inequalities, which have been obtained by J. Wilker [11] and C. Huygens [4], have attracted attention of several researchers (see, e.g., [1], [3], [6], [7], [8], [9], [10], [12], [13], [14], [15], [16]). In this paper we offer several refinements and generalizations of these results. Mathematics subject classification (2010): 26D05, 33B10.

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ژورنال

عنوان ژورنال: Pure Mathematics

سال: 2018

ISSN: 2160-7583,2160-7605

DOI: 10.12677/pm.2018.82020