Skip to main content Accessibility help
×
Home

The Radius of Convexity of a Linear Combination of Functions in or uα

  • Douglas Michael Campbell (a1)

Extract

Labelle and Rahman [4] showed that if f , g, the normalized convex functions in the unit disc D, then has a radius of convexity at least as large as the smallest root of 1 – 3r + 2r2 — 2r3 = 0. Their method requires neither the properties of the arithmetic mean nor the strong geometric properties of ; indeed, the procedure works for a linear combination of functions from any linear invariant family of finite order.

    • 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.

      The Radius of Convexity of a Linear Combination of Functions in or uα
      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.

      The Radius of Convexity of a Linear Combination of Functions in or uα
      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.

      The Radius of Convexity of a Linear Combination of Functions in or uα
      Available formats
      ×

Copyright

References

Hide All
1. Campbell, D. M., Locally univalent functions with locally univalent derivatives, Trans. Amer. Math. Soc. 162 (1971), 395409.
2. Campbell, D. M., β-close-to-bounded boundary rotation functions I. (to appear).
3. Goluzin, G. M., Geometric theory of functions of a complex variable, Amer. Math. Soc. Vol. 26 (Providence, R. I., 1969).
4. Labelle, G. and Rahman, Q. I., Remarque sur la moyenne arithmétique de fonctions univalentes convexes, Can. J. Math. 21 (1969), 977981.
5. Pommerenke, C., Linear-invariante Familien Analytischer Funktionen. I, Math. Ann. 155 (1964), 108154.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

The Radius of Convexity of a Linear Combination of Functions in or uα

  • Douglas Michael Campbell (a1)

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