Department
Mathematics
Document Type
Article
Publication Source
International Journal of Mathematics and Mathematical Sciences
Publication Date
1996-01-01
Volume
19
Issue
4
First Page
789
Last Page
795
Abstract
We study the problem maxh∊Sℜ[h(z1) + h(z2)] with z1, z2 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 [formula omitted] or z1, z2 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(z1) or f(z2) 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 z1 and z2 are both real numbers and z1z2 < 0. © 1996, Hindawi Publishing Corporation. All rights reserved.
Keywords
Quadratic Differential, Support Points, Univalent Functions
DOI
10.1155/S0161171296001093
Recommended Citation
Hibschweiler, Intisar Qumsiyeh, "Univalent Functions Maximizing Re[f(ζ1)+f(ζ2)]" (1996). Articles & Book Chapters. 436.
https://digitalcommons.daemen.edu/faculty_scholar/436
https://doi.org/10.1155/S0161171296001093
Comments
© 1996 Hindawi Publishing Corporation.
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.