广义三角函数与双曲函数对偶的应用II

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Mathematical Inequalities Pub Date : 2022-03-13 DOI:10.7153/jmi-2022-16-102

Hiroki Miyakawa, S. Takeuchi

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引用次数: 4

摘要

广义三角函数和广义双曲函数可以用作者先前发现的对偶公式相互转换。本文应用对偶公式证明了广义函数的wilker型不等式、huygens型不等式和(松弛的)cusa - huygens型不等式的对偶对。此外，还给出了先前未得到的多角和双角公式。

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Applications of a duality between generalized trigonometric and hyperbolic functions II

Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed) Cusa-Huygens-type inequalities for the generalized functions. In addition, multiple- and double-angle formulas not previously obtained are also given.

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来源期刊

Journal of Mathematical Inequalities MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.90

自引率

3.40%

发文量

审稿时长

6-12 weeks

期刊介绍： The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts. ''JMI'' is published quarterly; in March, June, September, and December.