AN APPLICATION OF SCHUR’S ALGORITHM TO VARIABILITY REGIONS OF CERTAIN ANALYTIC FUNCTIONS II
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Abstract We extend our study of variability regions, Ali et al. [‘An application of Schur algorithm to variability regions of certain analytic functions–I’, Comput. Methods Funct. Theory, to appear] from convex domains to starlike domains. Let $\mathcal {CV}(\Omega )$ be the class of analytic functions f in ${\mathbb D}$ with $f(0)=f'(0)-1=0$ satisfying $1+zf''(z)/f'(z) \in {\Omega }$ . As an application of the main result, we determine the variability region of $\log f'(z_0)$ when f ranges over $\mathcal {CV}(\Omega )$ . By choosing a particular $\Omega $ , we obtain the precise variability regions of $\log f'(z_0)$ for some well-known subclasses of analytic and univalent functions.
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1973 ◽
Vol 25
(2)
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pp. 420-425
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2014 ◽
Vol 98
(2)
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pp. 257-280
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1972 ◽
Vol 17
(1)
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pp. 1-29
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