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Koebe Domains for the Classes of Functions with Ranges Included in Given Sets
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L. Koczan
Published/Copyright:
June 9, 2010
Abstract
In this paper we present a new method of determining Koebe domains. We apply this method by giving a new proof of the well-known theorem of A. W. Goodman concerning the Koebe domain for the class T of typically real functions. We applied also the method to determine Koebe sets for classes of the special type, i.e. for TM,g = {ƒ ∈ T: ƒ(Δ) ⊂ Mg(Δ)}, g ∈ T ∩ S, M > 1, where Δ = {z ∈ C: |z| < 1} and T, S stand for the classes of typically real functions and univalent functions respectively. In particular, we find the Koebe domains for the class TM of all typically real and bounded functions, and for the class T(M) of all typically real functions with ranges in a given strip.
Received: 2007-03-12
Revised: 2007-09-04
Published Online: 2010-06-09
Published in Print: 2008-June
© Heldermann Verlag
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Articles in the same Issue
- Finite Partitions of Topological Groups into Congruent Thick Subsets
- Derivatives of Markov Kernels and Their Jordan Decomposition
- Sufficiency and Duality in Control Problems with Generalized Invexity
- Koebe Domains for the Classes of Functions with Ranges Included in Given Sets
- Upper and Lower Solutions Method for Fourth-Order Periodic Boundary Value Problems
- Efficiency and Duality for Generalized Convex Multiobjective Programming
- General Mixed Vector F-Implicit Complementarity Problems in Banach Spaces
- Modelling and Products of Singularities in Colombeau's Algebra
- Set Differential Equations in Fréchet Spaces
- Positive Solutions for a Class of Nonresonant m-Point Boundary Value Problems
- Second Order Duality in Multiobjective Programming
