IDEAS home Printed from https://ideas.repec.org/a/hin/jijmms/316305.html
   My bibliography  Save this article

Univalent functions maximizing Re [ f ( ζ 1 ) + f ( ζ 2 ) ]

Author

Listed:
  • Intisar Qumsiyeh Hibschweiler

Abstract

We study the problem max h ∈ S ℜ [ h ( z 1 ) + h ( z 2 ) ] with z 1 , z 2 in Δ . We show that no rotation of the Koebe function is a solution for this problem except possibly its real rotation, and only when z 1 = z ¯ 2 or z 1 , z 2 are both real, and are in a neighborhood of the x -axis. We prove that if the omitted set of the extremal function f is part of a straight line that passes through f ( z 1 ) or f ( z 2 ) then f is the Koebe function or its real rotation. We also show the existence of solutions that are not unique and are different from the Koebe function or its real rotation. The situation where the extremal value is equal to zero can occur and it is proved, in this case, that the Koebe function is a solution if and only if z 1 and z 2 are both real numbers and z 1 z 2 < 0 .

Suggested Citation

  • Intisar Qumsiyeh Hibschweiler, 1996. "Univalent functions maximizing Re [ f ( ζ 1 ) + f ( ζ 2 ) ]," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:316305
    DOI: 10.1155/S0161171296001093
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJMMS/19/316305.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJMMS/19/316305.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/S0161171296001093?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jijmms:316305. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.