Some Inequalities for the Generalized Trigonometric and Hyperbolic Functions

Li Yin^1, , Li-Guo Huang¹ and and Feng Qi^{2, 3}

¹Department of Mathematics, Binzhou University, Binzhou City, Shandong Province, China

²College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China

³Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, China;Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, China

Cite this paper:
Li Yin, Li-Guo Huang and and Feng Qi. Some Inequalities for the Generalized Trigonometric and Hyperbolic Functions. Turkish Journal of Analysis and Number Theory. 2014; 2(3):96-101. doi: 10.12691/tjant-2-3-8

Abstract

In the paper, the authors establish some inequalities of the generalized trigono-metric and hyperbolic functions, partially solve a conjecture posed by R. Klén, M. Vuorinen, and X.-H. Zhang, and finally pose an open problem.

Keywords:
inequality generalized trigonometric function generalized hyperbolic functions Bernoulli inequality Huygens' inequality Wilker's inequality conjecture open problem

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