Skip to main content Accessibility help
×
Home

Inequalities for symmetric means, symmetric harmonic means, and their applications

  • Hsu-Tung Ku (a1), Mei-Chin Ku (a1) and Xin-Min Zhang (a2)

Abstract

In this paper, we establish a number of inequalities involving symmetric means and symmetric harmonic means. We then apply these new inequalities to obtain many geometric inequalities of isoperimetric type for plane polygons.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Inequalities for symmetric means, symmetric harmonic means, and their applications
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Inequalities for symmetric means, symmetric harmonic means, and their applications
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Inequalities for symmetric means, symmetric harmonic means, and their applications
      Available formats
      ×

Copyright

References

Hide All
[1]Beckenbach, E.F. and Bellman, R., Inequalities (Springer-Verlag, Berlin, Heidelberg, New York, 1965).
[2]Brooks, R. and Wakesman, P., ‘The first eigenvalue of a scalene triangle’, Proc. Amer. Math. Soc. 100 (1987), 175182..
[3]Bullen, P.S., Mitrinović, D.S. and Vasić, P.M., Means and their inequalities (Reidel, Dordrecht, 1988).
[4]Hardy, G., Littlewood, J.E. and Pólya, G., Inequalities (Cambridge University Press, Cambridge, New York, 1951).
[5]Kazarinoff, M.D., Geometric inequalities, New Math. Library (Random House, New York, 1961).
[6]Ku, H.T., Ku, M.C. and Zhang, X.M., ‘Generalized power means and interpolating inequalities’, (preprint).
[7]Ku, H.T., Ku, M.C. and Zhang, X.M., ‘Analytic and geometric isoperimetric inequalities’, J. Geom. 53 (1995), 100121.
[8]Macnab, D.S., ‘Cyclic polygons and related questions’, Math. Gaz. 65 (1981), 2228.
[9]Mitrinović, D.S., Analytic inequalities (Springer-Verlag, Berlin, Heidelberg, New York, 1970).
[10]Mitrinović, D.S., Pečarić, J.E. and Fink, A.M., Classical and new inequalities in analysis (Kluwer Academic Publishers, Dordrecht, Boston, London, 1993).
[11]Mitrinović, D.S., Pečarić, J.E. and Volenec, V., Recent advances in geometric inequalities (Kluwer Academic Publishers, Dordrecht, Boston, London, 1989).
[12]Osserman, R., ‘The isoperimetric inequalities’, Bull. Amer. Math. Soc. 84 (1978), 11821238.
[13]Pólya, G., Mathematics and plausible reasoning I, Induction and Analogy in Mathematics (Princeton University Press, Princeton, NJ, 1954.).
[14]Pólya, G., ‘On the eigenvalues of vibrating membrances’, London Math. Soc. 11 (1961), 414433.
[15]Pólya, G. and Szegö, G., Isoperimetric inequalities in mathematical physics, Annals of Mathematics 27 (Princeton, NJ, 1951).
[16]Zhang, X.M., ‘Bonnesen-style inequalities and pseudo-perimeters for polygons’, J. Geom. (to appear).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Inequalities for symmetric means, symmetric harmonic means, and their applications

  • Hsu-Tung Ku (a1), Mei-Chin Ku (a1) and Xin-Min Zhang (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed