Sharpening and Generalizations of Carlson's Inequality for the Arc Cosine Function

Yıl 2010, Cilt: 39 Sayı: 3, 403 - 409, 01.03.2010

Bai-ni Guo Feng Qi

Anahtar Kelimeler

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Kaynakça

• Carlson, B. C. Inequality for a symmetric elliptic integral, Proc. Amer. Math. Soc. 25 (3), 698–703, 1970.
• Guo, B.-N. and Qi, F. Sharpening and generalizations of Carlson’s double inequality for the arc cosine function, Available online at http://arxiv.org/abs/0902.3039.
• Mitrinovi´c, D. S. Analytic Inequalities (Springer-Verlag, New York/Heidelburg/Berlin, 1970).
• Qi, F., Cui, L.-H. and Xu, S.-L. Some inequalities constructed by Tchebysheff ’s integral inequality, Math. Inequal. Appl. 2 (4), 517–528, 1999.
• Qi, F. and Guo, B.-N. A concise proof of Oppenheim’s double inequality relating to the cosine and sine functions, Available online at http://arxiv.org/abs/0902.2511.
• Qi, F. and Guo, B.-N. Concise sharpening and generalizations of Shafer’s inequality for the arc sine function, Available online at http://arxiv.org/abs/0902.2588.
• Qi, F. and Guo, B.-N. Sharpening and generalizations of Shafer-Fink’s double inequality for the arc sine function, Available online at http://arxiv.org/abs/0902.3036.
• Qi, F., Niu, D.-W. and Guo, B.-N. Refinements, generalizations, and applications of Jor- dan’s inequality and related problems, J. Inequal. Appl. 2009, 2009. Article ID 271923, 52 pages; Available online at http://dx.doi.org/10.1155/2009/271923.
• Qi, F., Zhang, Sh.-Q. and Guo, B.-N. Sharpening and generalizations of Shafer’s inequality for the arc tangent function, J. Inequal. Appl. 2009, 2009. Article ID 930294, 10 pages; Available online at http://dx.doi.org/10.1155/2009/930294.
• Zhang, Sh.-Q. and Guo, B.-N. Monotonicity results and inequalities for the inverse hyper
• bolic sine, Chinese Quart. J. Math. 24 (3), 394–388, 2009.