BibTex RIS Cite

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

Year 2012, Volume: 41 Issue: 2 , 201 - 209 , 01.02.2012
https://izlik.org/JA57KC28JR

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
https://izlik.org/JA57KC28JR

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
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
IZ https://izlik.org/JA57KC28JR
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. https://izlik.org/JA57KC28JR
AMA 1.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):201-209. https://izlik.org/JA57KC28JR
Chicago Zhao, J.-l., C.-f. Wei, B.-n. Guo, and F. Qi. 2012. “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”. Hacettepe Journal of Mathematics and Statistics 41 (2): 201-9. https://izlik.org/JA57KC28JR.
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 [1]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, Feb. 2012, [Online]. Available: https://izlik.org/JA57KC28JR
ISNAD 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 41/2 (February 1, 2012): 201-209. https://izlik.org/JA57KC28JR.
JAMA 1.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, Feb. 2012, pp. 201-9, https://izlik.org/JA57KC28JR.
Vancouver 1.J.-l. Zhao, C.-f. Wei, B.-n. Guo, F. Qi. Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function. Hacettepe Journal of Mathematics and Statistics [Internet]. 2012 Feb. 1;41(2):201-9. Available from: https://izlik.org/JA57KC28JR