BibTex RIS Kaynak Göster

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

Yıl 2012, Cilt: 41 Sayı: 2, 201 - 209, 01.02.2012

Kaynakça

  • 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

Yıl 2012, Cilt: 41 Sayı: 2, 201 - 209, 01.02.2012

Kaynakça

  • 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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Matematik
Yazarlar

J.-l. Zhao Bu kişi benim

C.-f. Wei Bu kişi benim

B.-n. Guo Bu kişi benim

F. Qi Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2012
Yayımlandığı Sayı Yıl 2012 Cilt: 41 Sayı: 2

Kaynak Göster

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. Şubat 2012;41(2):201-209.
Chicago Zhao, J.-l., C.-f. Wei, B.-n. Guo, ve F. Qi. “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”. Hacettepe Journal of Mathematics and Statistics 41, sy. 2 (Şubat 2012): 201-9.
EndNote Zhao J-l, Wei C-f, Guo B-n, Qi F (01 Şubat 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, ve F. Qi, “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”, Hacettepe Journal of Mathematics and Statistics, c. 41, sy. 2, ss. 201–209, 2012.
ISNAD Zhao, J.-l. vd. “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”. Hacettepe Journal of Mathematics and Statistics 41/2 (Şubat 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. vd. “Sharpening and Generalizations of Carlson’s Double Inequality for the Arc Cosine Function”. Hacettepe Journal of Mathematics and Statistics, c. 41, sy. 2, 2012, ss. 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.