Sharpened versions of Mitrinović-Adamović, Lazarević and Wilkers inequalities for trigonometric and hyperbolic functions
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Authors
Shan-He Wu
- Department of Mathematics, Longyan University, Longyan, Fujian, 364012, P. R. China.
Shu-Guang Li
- Department of Mathematics, Longyan University, Longyan, Fujian, 364012, P. R. China.
Mihály Bencze
- Department of Mathematics, University of Craiova, Craiova, RO-200585, Romania.
Abstract
In this paper, we establish new sharpened versions of Mitrinović-Adamović and Lazarević's inequalities.
Further, we provide an application of our results to the improvements of Wilker's inequality for trigonometric
and hyperbolic functions. We show that the coefficient assigned to each of these sharpened inequalities is
best possible.
Share and Cite
ISRP Style
Shan-He Wu, Shu-Guang Li, Mihály Bencze, Sharpened versions of Mitrinović-Adamović, Lazarević and Wilkers inequalities for trigonometric and hyperbolic functions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2688--2696
AMA Style
Wu Shan-He, Li Shu-Guang, Bencze Mihály, Sharpened versions of Mitrinović-Adamović, Lazarević and Wilkers inequalities for trigonometric and hyperbolic functions. J. Nonlinear Sci. Appl. (2016); 9(5):2688--2696
Chicago/Turabian Style
Wu, Shan-He, Li, Shu-Guang, Bencze, Mihály. "Sharpened versions of Mitrinović-Adamović, Lazarević and Wilkers inequalities for trigonometric and hyperbolic functions." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2688--2696
Keywords
- Mitrinović-Adamović's inequality
- Lazarević's inequality
- Wilker's inequality
- sharpening
- best possible coefficient
- trigonometric functions
- hyperbolic functions.
MSC
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