Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4632172 | Applied Mathematics and Computation | 2011 | 8 Pages |
Abstract
In the paper we consider the class Γ of analytic and univalent functions f in the unit disk Δ, normalized by f(0) = f′(0) − 1 = 0, having real coefficients and such that f(Δ) is convex in the direction of the real axis. We are especially interested in some subclasses of Γ. The most important of them is Γ(c) consisting of those functions which have the second coefficients of the Taylor expansion fixed and equal to c. We obtain the Koebe set for this class as well as for the classes Γ+(c) and Γ−(c) of functions which are in some sense convex in the direction of positive and negative axes respectively.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Leopold Koczan, Paweł Zaprawa,