广义三角函数与双曲函数的Wilker-Huygens型不等式
Wilker-Huygens Inequalities Involving Generalized Trigonometric and Hyperbolic Function
摘要:
主要研究了带有一个参数p的广义三角函数及广义双曲函数的Wilker型与Huygens型不等式，给出了广义三角函数与双曲函数的加强不等式。本文用极其简单的方法所获得的一些结果补充推广了已知结果。
Abstract:
This paper establishes Wilker-Huygens inequalities for generalized trigonometric and hyperbolic function with a parameter. And some classical inequalities for the generalized trigonometric and hyperbolic functions are generalized. The obtained results of this paper improve and complement some known results.
参考文献
|
[1]
|
Wilker, J.B. (1989) Problem E3306. The American Mathematical Monthly, 96, 55-57.
http://www.jstor.org/stable/2323260?origin=crossref [Google Scholar] [CrossRef]
|
|
[2]
|
Huygens, C. Oervres Completes. Societe Houondaise des Science, Haga, 1888-1940.
|
|
[3]
|
Neuman, E. (2012) On Wilker and Huygens Type Inequalities. Mathematical Inequalities & Applications, 15, 271-279. [Google Scholar] [CrossRef]
|
|
[4]
|
Zhu, L. (2005) A New Simple Proof of Wilker’s Inequalities. Mathematical Inequalities & Applications, 8, 749-750. [Google Scholar] [CrossRef]
|
|
[5]
|
Wu, S. (2009) On Extension and Refinement of Wilker’s Inequality. Rocky Mountain Journal of Mathematics, 39, 683-687. [Google Scholar] [CrossRef]
|
|
[6]
|
Zhu, L. (2007) On Wilker-Type In-equalities. Mathematical Inequalities & Applications, 10, 727-731. [Google Scholar] [CrossRef]
|
|
[7]
|
Neuman, E. and Sandor, J. (2010) On Some Inequalities Involving Trigonometric and Hyperbolic Function with Emphasis on the Cusa-Huygens, Wilker and Huygens Inequalities. Mathematical Inequalities & Applications, 13, 715-723. [Google Scholar] [CrossRef]
|
|
[8]
|
Lindqvist, P. (1995) Some Remarkable Sine and Cosine Functions. Ricerche di Mate-matica, 269-290.
|
|
[9]
|
Klén, R., Vuorinen, M. and Zhang, X.H. (2014) Inequalities for the Generalized Trigonometric and Hyperbolic Functions. Journal of Mathematical Analysis & Applications, 409, 521-529. [Google Scholar] [CrossRef]
|
|
[10]
|
Neuman, E. (2014) Inequalities Involving Generalized Trigonometric and Hyperbolic Functions. Journal of Mathematical Inequalities, 8, 725-736. [Google Scholar] [CrossRef]
|