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Star center points of starlike functions

Published online by Cambridge University Press:  09 April 2009

Louis Raymon  and
David E. Tepper
Louis Raymon
Affiliation:
Temple University, Philadelphia, Penna., U.S.A.
David E. Tepper
Affiliation:
The Institute for Advenced Studty, Priceton, N.J., U.S.A.
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Let be regular and unvivalent in the unit disk D and map D onto a region R. A point w0∈ R is called a star-center point of f(z), or of R, if tf(z)+(1−t)w0∈ R for z∈D and 0≦ t≦ 1. In this paper we consider only functions of the form (1) where w = 0 is a star-center point, i.e., those functions that are starlike with respect to the origin.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 4 , June 1975 , pp. 505 - 510
Copyright
Copyright © Australian Mathematical Society 1975

References

Nehari, Z., Conformal Mapping (1952), (McGraw-Hill, New York, 1952, MR 13, 640.)Google Scholar
Robertson, M. S. (1945), ‘Star center points of multivalent functions’, Duke Mahh. J. 12, 669–684; MR 7–379.Google Scholar
Suffridge, T. J. (1940), ‘Some remarks on convex maps of the unit disk’, Duke Math. J. 37, 775–777; MR 42–852.Google Scholar
Strohhäcker, E. (1933), ‘Beitrage zur Theorie der Schlichten Funcktionen’, Math. Z. 37, 336–380; Zbl. 7–214.Google Scholar