%0 Journal Article %T Sharp Stolarsky mean bounds for the complete elliptic integral of the second kind %A Yang, Zhen-Hang %A Chu, Yu-Ming %A Zhang, Xiao-Hui %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 3 %@ ISSN 2008-1901 %F Yang2017 %X In the article, we prove that the double inequality \[25/16<\varepsilon(r)/S_{5/2,2}(1,\acute{r})<\pi/2,\] holds for all \(r \in (0, 1)\) with the best possible constants \(25/16\) and \(\pi/2\), where \(\acute{r}=(1-r^2)^{1/2}, \varepsilon(r)=\int^{\pi/2}_0\sqrt{1-r^2\sin^2(t)}dt\) , is the complete elliptic integral of the second kind and \(S_{p,q}(a,b)=[q(a^p-b^p)/(p(a^q-b^q))]^{1/(p-q)}\), is the Stolarsky mean of a and b. %9 journal article %R 10.22436/jnsa.010.03.06 %U http://dx.doi.org/10.22436/jnsa.010.03.06 %P 929--936 %0 Book %T Handbook of mathematical functions with formulas, graphs, and mathematical tables %A M. Abramowitz %A I. A. Stegun %D 1964 %I National Bureau of Standards Applied Mathematics Series, For sale by the Superintendent of Documents, U.S. Government Printing Office %C Washington, D.C. %F Abramowitz1964 %0 Journal Article %T A monotonicity property involving \(_3F_2\) and comparisons of the classical approximations of elliptical arc length %A R. W. Barnard %A K. Pearce %A K. C. Richards %J SIAM J. Math. Anal. %D 2000 %V 32 %F Barnard2000 %0 Journal Article %T On the monotonity of certain functionals in the theory of analytic functions %A M. Biernacki %A J. Krzyz˙ %J Ann. Univ. Mariae Curie-Skłodowska. Sect. A. %D 1955 %V 9 %F Biernacki1955 %0 Journal Article %T Optimal Lehmer mean bounds for the Toader mean %A Y.-M. Chu %A M- K. Wang %J Results Math. %D 2012 %V 61 %F Chu2012 %0 Journal Article %T Bounds for complete elliptic integrals of the second kind with applications %A Y.-M. Chu %A M.-K. Wang %A S.-L. Qiu %A Y.-P. Jiang %J Comput. Math. Appl. %D 2012 %V 63 %F Chu2012 %0 Journal Article %T Minkowski-type inequalities for two variable Stolarsky means %A P. Czinder %A Z. Páles %J Acta Sci. Math. (Szeged) %D 2003 %V 69 %F Czinder2003 %0 Journal Article %T An extension of the Hermite-Hadamard inequality and an application for Gini and Stolarsky means %A P. Czinder %A Z. Páles %J JIPAM. J. Inequal. Pure Appl. Math. %D 2004 %V 5 %F Czinder2004 %0 Journal Article %T Some comparison inequalities for Gini and Stolarsky means %A P. Czinder %A Z. Páles %J Math. Inequal. Appl. %D 2006 %V 9 %F Czinder2006 %0 Journal Article %T Ratio of Stolarsky means: monotonicity and comparison %A L. Losonczi %J Publ. Math. Debrecen %D 2009 %V 75 %F Losonczi2009 %0 Journal Article %T On comparison of Stolarsky and Gini means %A E. Neuman %A Z. Páles %J J. Math. Anal. Appl. %D 2003 %V 278 %F Neuman2003 %0 Journal Article %T Inequalities involving Stolarsky and Gini means %A E. Neuman %A J. Sándor %J Math. Pannon %D 2003 %V 14 %F Neuman2003 %0 Book %T (Ed.) NIST handbook of mathematical functions %A F. W. J. Olver %A D. W. Lozier %A R. F. Boisvert %A C. W. Clark %D 2010 %I With 1 CD-ROM (Windows, Macintosh and UNIX). U.S. Department of Commerce, National Institute of Standards and Technology, Washington, DC; Cambridge University Press %C Cambridge %F Olver2010 %0 Journal Article %T On two problems concerning means %A S.-L. Qiu %A J.-M. Shen %J (Chinese) J. Hangzhou Inst. Electron. Eng. %D 1997 %V 17 %F Qiu1997 %0 Journal Article %T Generalizations of the logarithmic mean %A K. B. Stolarsky %J Math. Mag. %D 1975 %V 48 %F Stolarsky1975