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

Year 2012, Volume: 41 Issue: 2, 201 - 209, 01.02.2012

References

  • Carlson, B. C. Inequality for a symmetric elliptic integral, Proc. Amer. Math. Soc. 25 (3), 698–703, 1970.
  • Chen, C. -P., Cheung, W. -S. and Wang, W.-S. On Shafer and Carlson inequali- ties, J. Inequal. Appl. 2011, Article ID 840206, 10 pages, 2011; Available online at http://dx.doi.org/10.1155/2011/840206. [3] de Abreu, G. T. F. Arbitrarily tight upper and lower bounds on the Gaussian q-function and related functions, 2009 IEEE International Conference on Communications (ICC 2009), Vols 1-8, 1944–1949, Dresden, Germany, Jun. 14-18, 2009; Available online at http://dx.doi.org/10.1109/ICC.2009.5198762.
  • Fink, A. M. Two inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 6, 48–49, 1995.
  • 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.
  • Guo, B. -N. and Qi, F. Sharpening and generalizations of Carlson’s inequality for the arc cosine function, Hacet. J. Math. Stat. 39 (3), 403–409, 2010.
  • Maleˇsevi´c, B. J. An application of λ-method on Shafer-Fink’s inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 8, 90–92, 1997.
  • Mitrinovi´c, D. S. Analytic Inequalities (Springer-Verlag, Berlin, 1970).
  • Pan, W. -H. and Zhu, L. Generalizations of Shafer-Fink-type inequalities for the arc sine function, J. Inequal. Appl. 2009, Article ID 705317, 6 pages, 2009; Available online at http://dx.doi.org/10.1155/2009/705317. [10] 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. Sharpening and generalizations of Carlson’s inequality for the arc cosine function, Available online at http://arxiv.org/abs/0902.3495.
  • Qi, F. and Guo, B. -N. Sharpening and generalizations of Shafer’s inequality for the arc sine function, Integral Transforms Spec. Funct. 23 (2), 129–134, 2012; Available online at http://dx.doi.org/10.1080/10652469.2011.564578.
  • 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, Article ID 271923, 52 pages, 2009; Available online at http://dx.doi.org/10.1155/2009/271923.
  • Qi, F., Zhang, S. -Q. and Guo, B. -N. Sharpening and generalizations of Shafer’s inequality for the arc tangent function, J. Inequal. Appl. 2009, Article ID 930294, 9 pages, 2009; Available online at http://dx.doi.org/10.1155/2009/930294.
  • Zhang, S. -Q. and Guo, B. -N. Monotonicity results and inequalities for the inverse hyperbolic sine, Chinese Quart. J. Math. 24 (3), 394–388, 2009.
  • Zhu, L. A solution of a problem of Oppeheim, Math. Inequal. Appl. 10 (1), 57–61, 2007.

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

Year 2012, Volume: 41 Issue: 2, 201 - 209, 01.02.2012

References

  • Carlson, B. C. Inequality for a symmetric elliptic integral, Proc. Amer. Math. Soc. 25 (3), 698–703, 1970.
  • Chen, C. -P., Cheung, W. -S. and Wang, W.-S. On Shafer and Carlson inequali- ties, J. Inequal. Appl. 2011, Article ID 840206, 10 pages, 2011; Available online at http://dx.doi.org/10.1155/2011/840206. [3] de Abreu, G. T. F. Arbitrarily tight upper and lower bounds on the Gaussian q-function and related functions, 2009 IEEE International Conference on Communications (ICC 2009), Vols 1-8, 1944–1949, Dresden, Germany, Jun. 14-18, 2009; Available online at http://dx.doi.org/10.1109/ICC.2009.5198762.
  • Fink, A. M. Two inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 6, 48–49, 1995.
  • 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.
  • Guo, B. -N. and Qi, F. Sharpening and generalizations of Carlson’s inequality for the arc cosine function, Hacet. J. Math. Stat. 39 (3), 403–409, 2010.
  • Maleˇsevi´c, B. J. An application of λ-method on Shafer-Fink’s inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 8, 90–92, 1997.
  • Mitrinovi´c, D. S. Analytic Inequalities (Springer-Verlag, Berlin, 1970).
  • Pan, W. -H. and Zhu, L. Generalizations of Shafer-Fink-type inequalities for the arc sine function, J. Inequal. Appl. 2009, Article ID 705317, 6 pages, 2009; Available online at http://dx.doi.org/10.1155/2009/705317. [10] 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. Sharpening and generalizations of Carlson’s inequality for the arc cosine function, Available online at http://arxiv.org/abs/0902.3495.
  • Qi, F. and Guo, B. -N. Sharpening and generalizations of Shafer’s inequality for the arc sine function, Integral Transforms Spec. Funct. 23 (2), 129–134, 2012; Available online at http://dx.doi.org/10.1080/10652469.2011.564578.
  • 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, Article ID 271923, 52 pages, 2009; Available online at http://dx.doi.org/10.1155/2009/271923.
  • Qi, F., Zhang, S. -Q. and Guo, B. -N. Sharpening and generalizations of Shafer’s inequality for the arc tangent function, J. Inequal. Appl. 2009, Article ID 930294, 9 pages, 2009; Available online at http://dx.doi.org/10.1155/2009/930294.
  • Zhang, S. -Q. and Guo, B. -N. Monotonicity results and inequalities for the inverse hyperbolic sine, Chinese Quart. J. Math. 24 (3), 394–388, 2009.
  • Zhu, L. A solution of a problem of Oppeheim, Math. Inequal. Appl. 10 (1), 57–61, 2007.
There are 16 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

J.-l. Zhao This is me

C.-f. Wei This is me

B.-n. Guo This is me

F. Qi This is me

Publication Date February 1, 2012
Published in Issue Year 2012 Volume: 41 Issue: 2

Cite

APA Zhao, J.-l., Wei, C.-f., Guo, B.-n., Qi, F. (2012). Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function. Hacettepe Journal of Mathematics and Statistics, 41(2), 201-209.
AMA Zhao Jl, Wei Cf, Guo Bn, Qi F. Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function. Hacettepe Journal of Mathematics and Statistics. February 2012;41(2):201-209.
Chicago Zhao, J.-l., C.-f. Wei, B.-n. Guo, and F. Qi. “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”. Hacettepe Journal of Mathematics and Statistics 41, no. 2 (February 2012): 201-9.
EndNote Zhao J-l, Wei C-f, Guo B-n, Qi F (February 1, 2012) Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function. Hacettepe Journal of Mathematics and Statistics 41 2 201–209.
IEEE J.-l. Zhao, C.-f. Wei, B.-n. Guo, and F. Qi, “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, pp. 201–209, 2012.
ISNAD Zhao, J.-l. et al. “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”. Hacettepe Journal of Mathematics and Statistics 41/2 (February 2012), 201-209.
JAMA Zhao J-l, Wei C-f, Guo B-n, Qi F. Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function. Hacettepe Journal of Mathematics and Statistics. 2012;41:201–209.
MLA Zhao, J.-l. et al. “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, 2012, pp. 201-9.
Vancouver Zhao J-l, Wei C-f, Guo B-n, Qi F. Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function. Hacettepe Journal of Mathematics and Statistics. 2012;41(2):201-9.