Bull. Austral. Math. Soc. 72(1) pp.87--107, 2005.
On the Ky Fan inequality and related inequalities II
Edward Neuman |
József Sándor |
.
Abstract
Ky Fan type inequalities for means of two or more variables are obtained. Refinements and improvements of known inequalities are derived. Applications to symmetric elliptic integrals of the first and second kind are also included.
Click to download PDF of this article (free access until July 2006)
or get the no-frills version
[an error occurred while processing this directive](Metadata: XML, RSS, BibTeX) | MathSciNet: MR2162296 | Z'blatt-MATH: 02212188 |
References
- H. Alzer;
Inequalities for arithmetic, geometric and harmonic means,
Bull. London Math. Soc. 22 (1990), pp. 362--366. MR1058313 - H. Alzer;
The inequality of Ky Fan and related results,
Acta Appl. Math. 38 (1995), pp. 305--354. MR1326638 - E.F. Beckenbach and R. Bellman;
Inequalities (Springer-Verlag, New York, 1965). MR192009 - B.C. Carlson;
Special functions of applied mathematics (Academic Press, New York, 1977). MR590943 - F. Chan, D. Goldberg and S. Gonek;
On extensions of an inequality among means,
Proc. Amer. Math. Soc. 42 (1974), pp. 202--207. MR338295 - E. El-Neweihi and F. Proschan;
Unified treatment of some inequalities among means,
Proc. Amer. Math. Soc. 81 (1981), pp. 388--390. MR597647 - I. Gavrea and T. Trif;
On Ky Fan's inequality,
Math. Inequal. Appl. 4 (2001), pp. 223--230. MR1823742 - G. Gini;
Di una formula comprensiva delle medie,
Metron 13 (1938), pp. 3--22. - V. Govedarica and M. Jovanović;
On the inequalities of Ky Fan, Wang--Wang and Alzer,
J. Math. Anal. Appl. 270 (2002), pp. 709--712. MR1916604 - G.H. Hardy, J.E. Littlewood and G. Pólya;
Inequalities,
(2nd edition) (Cambridge Univ. Press, London and New York, 1952). MR46395 - N. Levinson;
Generalization of an inequality of Ky Fan,
J. Math. Anal. Appl. 8 (1964), pp. 133--134. MR156928 - D.S. Mitrinović;
Analytic inequalities (Springer-Verlag, Berlin, 1970). MR274686 - E. Neuman;
Bounds for symmetric elliptic integrals,
J. Approx. Theory 122 (2003), pp. 249--259. MR1988303 - E. Neuman, C.E.M. Pearce, J. Pečarić and V. Šimić;
The generalized Hadamard inequality, g-convexity and functional Stolarsky means,
Bull. Austral. Math. Soc. 68 (2003), pp. 303--316. MR2016305 - E. Neuman and J. Sándor;
On the Ky Fan inequality and related inequalities I,
Math. Inequal. Appl. 5 (2002), pp. 49--56. MR1880271 - E. Neuman and J. Sándor;
Inequalities involving Stolarsky and Gini means,
Math. Pannon. 14 (2003), pp. 29--44. MR1960877 - E. Neuman and J. Sándor;
On the Schwab--Borchardt mean,
Math. Pannon. 14 (2003), pp. 253--266. MR2079318 - J. Pečarić and V. Šimić;
Stolarsky--Tobey mean in n variables,
Math. Inequal. Appl. 2 (1999), pp. 325--341. MR1698378 - J. Sándor;
Sur la fonction Gamma,
Publ. Centre. Rrech. Math. Pures., Neuchâtel, Ser. I 21 (1989), pp. 4--7. - J. Sándor;
On an inequality of Ky Fan,
(Preprint 90-7, Babes-Bolyai Univ.), pp. 29--34. MR1168048 - J. Sándor;
On the identric and logarithmic means,
Aequationes Math. 40 (1990), pp. 261--270. MR1069798 - J. Sándor and T. Trif;
A new refinement of the Ky Fan inequality,
Math. Inequal. Appl. 2 (1999), pp. 529--533. MR1717045 - K.B. Stolarsky;
Generalizations of the logarithmic mean,
Math. Mag. 48 (1975), pp. 87--92. MR357718 - W.-L. Wang and P.-F. Wang;
A class of inequalities for symmetric functions,
(in Chinese),
Acta Math. Sinica 27 (1984), pp. 485--497. MR767323
ISSN 0004-9727