Wilker-Huygens Inequalities Involving Generalized Trigonometric and Hyperbolic Function
نویسندگان
چکیده
منابع مشابه
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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The Huygens-Wilker type inequalities involving generalized trigonometric functions and generalized hyperbolic functions are established. The first and the second inequalities of Huygens and Wilker, for classes of functions under discussion, are also investigated.
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The authors obtain some Wilker and Cusa type inequalities for generalized trigonometric and hyperbolic functions and generalize some known inequalities.
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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.
متن کاملOn 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