# Inequalities for the generalized trigonometric and hyperbolic functions with two parameters

Volume 8, Issue 4, pp 315--323
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### Authors

Li Yin - Department of Mathematics, Binzhou University, Binzhou City, 256603 Shandong Province, China. Li-Guo Huang - Department of Mathematics, Binzhou University, Binzhou City, 256603 Shandong Province, China.

### Abstract

In this paper, we present some integral identities and inequalities of $(p; q)$-complete elliptic integrals, and prove some inequalities for the generalized trigonometric and hyperbolic functions with two parameters.

### Share and Cite

##### ISRP Style

Li Yin, Li-Guo Huang, Inequalities for the generalized trigonometric and hyperbolic functions with two parameters, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 4, 315--323

##### AMA Style

Yin Li, Huang Li-Guo, Inequalities for the generalized trigonometric and hyperbolic functions with two parameters. J. Nonlinear Sci. Appl. (2015); 8(4):315--323

##### Chicago/Turabian Style

Yin, Li, Huang, Li-Guo. "Inequalities for the generalized trigonometric and hyperbolic functions with two parameters." Journal of Nonlinear Sciences and Applications, 8, no. 4 (2015): 315--323

### Keywords

• complete elliptic integrals
• inequality
• generalized trigonometric function
• generalized hyperbolic function
• Fubini theorem.

•  33B10
•  33E05

### References

• [1] H. Alzer, Sharp inequalities for the complete elliptic integrals of the first kinds, Math. Proc. Camb. Phil. Soc., 124 (1988), 309-314.

• [2] G. D. Anderson, P. Duren, M. K. Vamanamurthy, An inequality for complete elliptic integrals, J. Math. Anal. Appl., 182 (1994), 257-259.

• [3] G. D. Anderson, S. L. Qiu, M. K. Vamanamurthy , Elliptic integrals inequalities, with applications , Constr. Approx., 14 (1998), 195-207.

• [4] G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen, Topics in special functions, arXiv:0712.3856v1[math.CA]. , ()

• [5] B. A. Bhayo, M. Vuorinen, Inequalities for eigenfunctions of the p-Laplacian, Issues of Analysis, http://arxiv.org/abs/1101.3911 , 20:2 (2013), 19 pages.

• [6] B. A. Bhayo, M. Vuorinen, On generalized trigonometric functions with two parameters, J. Approx. Theory, 164 (2012), 1415-1426.

• [7] S. Takeuchi, Generalized Jacobian elliptic functions and their application to bifurcation problems associated with p-Laplacian, J. Math. Anal. Appl., 385 (2012), 24-35.

• [8] M. K. Wang, Y. M. Chu , Asymptotical bounds for complete elliptic integrals of second kind, arXiv:1209. 0066v1[math.CA]., ()

• [9] L. Yin, L. G. Huang , Some properties related to generalized trigonometric and hyperbolic functions with two parameters, RGMIA Res. Rep. Coll., Art.143. http://rgmia.org/v17.php (2014)