A weighted and exponential generalization of Wilker's inequality and its applications

Integral Transforms and Special Functions

Volumn 18, Issue 8, 2007, Pages 529-535

  Wu, Shan He ^a   Srivastava, H M ^b  

^a LONGYAN UNIVERSITY   (China)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Exponential generalization; Huygens's inequality; S ndor Bencze conjectured inequality; Weighted generalization; Weighted inequalities; Wilker's inequality

Indexed keywords

EID: 34547986923     PISSN: 10652469     EISSN: 14768291     Source Type: Journal    
DOI: 10.1080/10652460701284164     Document Type: Article

References (12)

1. Wilker, J.B., 1989, Problem E3306. American Mathematical Monthly, 96, 55.
2. Sumner, J.S., Jagers, A.A., Vowe, M. and Anglesio, J., 1991, Inequalities involving trigonometric functions. American Mathematical Monthly, 98, 264-267.
3. Guo, B.-N., Li, W. and Qi, F., 2003, Proofs of Wilker's inequalities involving trigonometric functions. In Chinju and Masan (Eds) Inequality Theory and Applications, Vol. 2 (Nova Science Publishers, Hauppauge, New York), pp. 109-112.
4. Guo, B.-N., Li, W., Qiao, B.-M. and Qi, F., 2000, On new proofs of inequalities involving trigonometric functions. RGMIA Research Report Collection, 3(1). Available online at URL: http://rgm.ia.vu.edu.au/ v3n1.html.
5. Guo, B.-N., Qiao, B.-M., Qi, R and Li, W., 2003, On new proofs of Wilker's inequalities involving trigonometric functions. Mathematical Inequalities and Applications, 6, 19-22.
6. Qi, F., 2006, Jordan's inequality: Refinements, generalizations, applications and related problems. RGMIA Research Report Collection, 9(3). Available online at URL: http://rgmia.vu.edu.au/v9n3.html.
7. Pinelis, I., 2004, l'Hôpital rules for monotonicity and the Wilker-Anglesio inequality. American Mathematical Monthly, 111, 905-909.
8. Zhu, L., 2005, A new simple proof of Wilker's inequality. Mathematical Inequalities and Applications, 8, 749-750.
9. Huygens, C., 1888-1940, Oeuvres Completes, Vols. 1-20 (Publiées par la Société Hollandaise des Science, Haga).
10. Sándor, J. and Bencze, M., 2005, On Huygens's trigonometric inequality, RGMIA Research Report Collection, 8(3). Available online at URL: http://rgm.ia.vu.edu.au/v8n3.html.
11. Hardy, G.H., Littlewood, J.E. and Pólya, G., 1952, Inequalities (2nd edn) (Cambridge University Press, Cambridge).
12. Mitrinovic̀, D.S. and Vasić, P.M., 1970, Analytic Inequalities (Springer-Verlag, New York).