On some new Wilker and Huygens type trigonometric‐hyperbolic inequalities
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The hyperbolic counterparts of the Wilker and Huygens trigonometric inequalities have been introduced by L. Zhu [5] and E. Neuman - J. S´andor [2]. Here we shall study certain new inequalities of Wilker and Huygens type, involving the trigonometric function sin x and the hyperbolic function sinh x. Multiplicative analogues of the stated inequalities are pointed out, too.
Abstract
The hyperbolic counterparts of the Wilker and Huygens trigonometric inequalities have been introduced by L. Zhu [5] and E. Neuman - J. S´andor [2]. Here we shall study certain new inequalities of Wilker and Huygens type, involving the trigonometric function sin x and the hyperbolic function sinh x. Multiplicative analogues of the stated inequalities are pointed out, too.
참고문헌 (5)
- R. Kl´en, "On Jordan type inequalities for hyperbolic functions", Journal of Inequalities and Applications, pp.14~ (2010)
- E. Neuman, "On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities", Mathematical Inequalities and Applications, 13(4), pp.715~723 (2010)
- J. S´andor, "On the inequality of means (Romanian)", Lucr. Semin. Did. Mat., 14, pp.232~235 (1998)
- S. Wu, "A weighted and exponential generalization of Wilker inequality and its applications", Integral Transf. Spec. Funct, 18(8), pp.525~535 (2007)
- L. Zhu, "On Wilker type inequalities", Math. Ineq. Appl, 10(4), pp.727~731 (2007)