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On the Ky Fan inequality and related inequalities II

Published online by Cambridge University Press:  17 April 2009

Edward Neuman
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901–4408, United States of America, e-mail: edneuman@math.siu.edu, urladdr: http://www.math.siu.edu/neuman/personal.html
József Sándor
Affiliation:
Department of Pure Mathematics, Babes-Bolyai University, Ro-3400 Cluj-Napoca, Romania, e-mail: jsandor@math.ubbcluj.ro
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Alzer, H., ‘Inequalities for arithmetic, geometric and harmonic means’, Bull. London Math. Soc. 22 (1990), 362366.CrossRefGoogle Scholar
[2]Alzer, H., ‘The inequality of Ky Fan and related results’, Acta Appl. Math. 38 (1995), 305354.CrossRefGoogle Scholar
[3]Beckenbach, E.F. and Bellman, R., Inequalities (Springer-Verlag, New York, 1965).CrossRefGoogle Scholar
[4]Carlson, B.C., Special functions of applied mathematics (Academic Press, New York, 1977).Google Scholar
[5]Chan, F., Goldberg, D. and Gonek, S., ‘On extensions of an inequality among means’, Proc. Amer. Math. Soc. 42 (1974), 202207.CrossRefGoogle Scholar
[6]El-Neweihi, E. and Proschan, F., ‘Unified treatment of some inequalities among means’, Proc. Amer. Math. Soc. 81 (1981), 388390.CrossRefGoogle Scholar
[7]Gavrea, I. and Trif, T., ‘On Ky Fan's inequality’, Math. Inequal. Appl. 4 (2001), 223230.Google Scholar
[8]Gini, G., ‘Di una formula comprensiva delle medie’, Metron 13 (1938), 322.Google Scholar
[9]Govedarica, V. and Jovanović, M., ‘On the inequalities of Ky Fan, Wang-Wang and Alzer’, J. Math. Anal. Appl. 270 (2002), 709712.CrossRefGoogle Scholar
[10]Hardy, G.H., Littlewood, J.E. and Pólya, G., Inequalities, (2nd edition) (Cambridge Univ. Press, London and New York, 1952).Google Scholar
[11]Levinson, N., ‘Generalization of an inequality of Ky Fan’, J. Math. Anal. Appl. 8 (1964), 133134.CrossRefGoogle Scholar
[12]Mitrinović, D.S., Analytic inequalities (Springer-Verlag, Berlin, 1970).CrossRefGoogle Scholar
[13]Neuman, E., ‘Bounds for symmetric elliptic integrals’, J. Approx. Theory 122 (2003), 249259.CrossRefGoogle Scholar
[14]Neuman, E., Pearce, C.E.M., Pečarić, J. and Šimić, V., ‘The generalized Hadamard inequality, g-convexity and functional Stolarsky means’, Bull. Austral. Math. Soc. 68 (2003), 303316.CrossRefGoogle Scholar
[15]Neuman, E. and Sándor, J., ‘On the Ky Fan inequality and related inequalities I’, Math. Inequal. Appl. 5 (2002), 4956.Google Scholar
[16]Neuman, E. and Sándor, J., ‘Inequalities involving Stolarsky and Gini means’, Math. Pannon. 14 (2003), 2944.Google Scholar
[17]Neuman, E. and Sándor, J., ‘On the Schwab-Borchardt mean’, Math. Pannon. 14 (2003), 253266.Google Scholar
[18]Pečarić, J. and Šimić, V., ‘Stolarsky-Tobey mean in n variables’, Math. Inequal. Appl. 2 (1999), 325341.Google Scholar
[19]Sándor, J., ‘Sur la fonction Gamma’, Publ. Centre. Rrech. Math. Pures., Neuchâtel, Ser. I 21 (1989), 47.Google Scholar
[20]Sándor, J., ‘On an inequality of Ky Fan’, (Preprint 90–7, Babes-Bolyai Univ.), pp. 2934.Google Scholar
[21]Sándor, J., ‘On the identric and logarithmic means’, Aequationes Math. 40 (1990), 261270.CrossRefGoogle Scholar
[22]Sándor, J. and Trif, T., ‘A new refinement of the Ky Fan inequality’, Math. Inequal. Appl. 2 (1999), 529533.Google Scholar
[23]Stolarsky, K.B., ‘Generalizations of the logarithmic mean’, Math. Mag. 48 (1975), 8792.CrossRefGoogle Scholar
[24]Wang, W.-L. and Wang, P.-F., ‘A class of inequalities for symmetric functions’, (in Chinese), Acta Math. Sinica 27 (1984), 485497.Google Scholar