Region of variability of two subclasses of univalent functions |
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Authors: | S Ponnusamy A Vasudevarao |
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Affiliation: | Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India |
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Abstract: | Let F1 (F2 respectively) denote the class of analytic functions f in the unit disk |z|<1 with f(0)=0=f′(0)−1 satisfying the condition RePf(z)<3/2 (RePf(z)>−1/2 respectively) in |z|<1, where Pf(z)=1+zf″(z)/f′(z). For any fixed z0 in the unit disk and λ∈0,1), we shall determine the region of variability for logf′(z0) when f ranges over the class and , respectively. |
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Keywords: | Analytic Univalent Close-to-convex Starlike functions Variability region |
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