Region of Variability for Exponentially Convex Univalent Functions |
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Authors: | Ponnusamy Saminathan Vasudevarao Allu M Vuorinen |
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Institution: | 1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India 2. Department of Mathematics, University of Turku, 20014, Turku, Finland
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Abstract: | For ${\alpha\in\mathbb C{\setminus}\{0\}}For
a ? \mathbb C\{0}{\alpha\in\mathbb C{\setminus}\{0\}} let E(a){\mathcal{E}(\alpha)} denote the class of all univalent functions f in the unit disk
\mathbbD{\mathbb{D}} and is given by f(z)=z+a2z2+a3z3+?{f(z)=z+a_2z^2+a_3z^3+\cdots}, satisfying
${\rm Re}\left (1+ \frac{zf'(z)}{f'(z)}+\alpha zf'(z)\right ) > 0 \quad {\rm in }\,{\mathbb D}.${\rm Re}\left (1+ \frac{zf'(z)}{f'(z)}+\alpha zf'(z)\right ) > 0 \quad {\rm in }\,{\mathbb D}. |
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Keywords: | |
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