| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2014-09-29T09:16:22Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143938 |
| . |
| Reference:
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