Inequalities for the generalized trigonometric and hyperbolic functions with two parameters

Volume 8, Issue 4, pp 315--323 http://dx.doi.org/10.22436/jnsa.008.04.04

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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.

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Keywords

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

MSC

•  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)