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Title: Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points (English)
Author: Yagmur, Nihat
Author: Orhan, Halit
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 139
Issue: 3
Year: 2014
Pages: 485-509
Summary lang: English
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Category: math
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Summary: The authors obtain the Fekete-Szegő inequality (according to parameters $s$ and $t$ in the region $s^{2}+st+t^{2}<3$, $s\neq t$ and $s+t\neq 2$, or in the region $s^{2}+st+t^{2}>3,$ $s\neq t$ and $s+t\neq 2$) for certain normalized analytic functions $f(z)$ belonging to $k\text {\rm -UST}_{\lambda ,\mu }^{n}(s,t,\gamma )$ which satisfy the condition \begin {equation*} \Re \bigg \{ \frac {(s-t)z ( D_{\lambda ,\mu }^{n}f(z))'} {D_{\lambda ,\mu }^{n}f(sz)-D_{\lambda ,\mu }^{n}f(tz)}\bigg \} >k \biggl \vert \frac {(s-t)z ( D_{\lambda ,\mu }^{n}f(z))'}{D_{\lambda ,\mu }^{n}f(sz)-D_{\lambda ,\mu }^{n}f(tz)}{-1} \biggr \vert +\gamma , \quad z\in \mathcal {U} . \end {equation*} Also certain applications of the main result a class of functions defined by the Hadamard product (or convolution) are given. As a special case of this result, the Fekete-Szegő inequality for a class of functions defined through fractional derivatives is obtained. (English)
Keyword: Fekete-Szeg\H {o} problem
Keyword: Sakaguchi function
Keyword: uniformly starlike function
Keyword: symmetric point
MSC: 30C45
MSC: 30C50
idZBL: Zbl 06391467
idMR: MR3269370
DOI: 10.21136/MB.2014.143938
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Date available: 2014-09-29T09:16:22Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/143938
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