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  • Bulletin of the Australian Mathematical Society, Volume 72, Issue 1
  • August 2005, pp. 87-107

On the Ky Fan inequality and related inequalities II

  • Edward Neuman (a1) and József Sándor (a2)
  • DOI: http://dx.doi.org/10.1017/S0004972700034894
  • Published online: 01 April 2009
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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]H. Alzer , ‘Inequalities for arithmetic, geometric and harmonic means’, Bull. London Math. Soc. 22 (1990), 362366.

[2]H. Alzer , ‘The inequality of Ky Fan and related results’, Acta Appl. Math. 38 (1995), 305354.

[3]E.F. Beckenbach and R. Bellman , Inequalities (Springer-Verlag, New York, 1965).

[5]F. Chan , D. Goldberg and S. Gonek , ‘On extensions of an inequality among means’, Proc. Amer. Math. Soc. 42 (1974), 202207.

[6]E. El-Neweihi and F. Proschan , ‘Unified treatment of some inequalities among means’, Proc. Amer. Math. Soc. 81 (1981), 388390.

[9]V. Govedarica and M. Jovanović , ‘On the inequalities of Ky Fan, Wang-Wang and Alzer’, J. Math. Anal. Appl. 270 (2002), 709712.

[11]N. Levinson , ‘Generalization of an inequality of Ky Fan’, J. Math. Anal. Appl. 8 (1964), 133134.

[12]D.S. Mitrinović , Analytic inequalities (Springer-Verlag, Berlin, 1970).

[13]E. Neuman , ‘Bounds for symmetric elliptic integrals’, J. Approx. Theory 122 (2003), 249259.

[21]J. Sándor , ‘On the identric and logarithmic means’, Aequationes Math. 40 (1990), 261270.

[23]K.B. Stolarsky , ‘Generalizations of the logarithmic mean’, Math. Mag. 48 (1975), 8792.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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