Region of variability for spiral-like functions with respect to a boundary point
S. Ponnusamy ; A. Vasudevarao ; M. Vuorinen
Colloquium Mathematicae, Tome 116 (2009), p. 31-46 / Harvested from The Polish Digital Mathematics Library
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For μ ∈ ℂ such that Re μ > 0 let ℱμ denote the class of all non-vanishing analytic functions f in the unit disk with f(0) = 1 and Re(2π/μzf'(z)/f(z)+(1+z)/(1-z))>0 in . For any fixed z₀ in the unit disk, a ∈ ℂ with |a| ≤ 1 and λ ∈ ̅, we shall determine the region of variability V(z₀,λ) for log f(z₀) when f ranges over the class ℱμ(λ)=f∈ℱμ:f'(0)=(μ/π)(λ-1)andf''(0)=(μ/π)(a(1-|λ|²)+(μ/π)(λ-1)²-(1-λ²)). In the final section we graphically illustrate the region of variability for several sets of parameters.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:283869 
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     title = {Region of variability for spiral-like functions with respect to a boundary point},
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     year = {2009},
     pages = {31-46},
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S. Ponnusamy; A. Vasudevarao; M. Vuorinen. Region of variability for spiral-like functions with respect to a boundary point. Colloquium Mathematicae, Tome 116 (2009) pp. 31-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-1-3/