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Region of variability of two subclasses of univalent functions
Authors:S Ponnusamy  A Vasudevarao
Affiliation:Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India
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 View the MathML source and View the MathML source, respectively.
Keywords:Analytic  Univalent  Close-to-convex  Starlike functions  Variability region
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