Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points

Nihat Yagmur; Halit Orhan

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 3, page 485-509
  • ISSN: 0862-7959

Abstract

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The authors obtain the Fekete-Szegő inequality (according to parameters s and t in the region s 2 + s t + t 2 < 3 , s ≠ t and s + t ≠ 2 , or in the region s 2 + s t + t 2 > 3 , s ≠ t and s + t ≠ 2 ) for certain normalized analytic functions f ( z ) belonging to k -UST λ , μ n ( s , t , γ ) which satisfy the condition ℜ ( s - t ) z ( D λ , μ n f ( z ) ) ' D λ , μ n f ( s z ) - D λ , μ n f ( t z ) > k ( s - t ) z ( D λ , μ n f ( z ) ) ' D λ , μ n f ( s z ) - D λ , μ n f ( t z ) - 1 + γ , z ∈ 𝒰 . 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.

How to cite

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Yagmur, Nihat, and Orhan, Halit. "Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points." Mathematica Bohemica 139.3 (2014): 485-509. <http://eudml.org/doc/261977>.

@article{Yagmur2014,
abstract = {The authors obtain the Fekete-Szegő inequality (according to parameters $s$ and $t$ in the region $s^\{2\}+st+t^\{2\}<3$, $s\ne t$ and $s+t\ne 2$, or in the region $s^\{2\}+st+t^\{2\}>3,$$s\ne t$ and $s+t\ne 2$) 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 \lbrace \frac\{(s-t)z ( D\_\{\lambda ,\mu \}^\{n\}f(z))^\{\prime \}\}\{D\_\{\lambda ,\mu \}^\{n\}f(sz)-D\_\{\lambda ,\mu \}^\{n\}f(tz)\}\bigg \rbrace >k \biggl \vert \frac\{(s-t)z ( D\_\{\lambda ,\mu \}^\{n\}f(z))^\{\prime \}\}\{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.},
author = {Yagmur, Nihat, Orhan, Halit},
journal = {Mathematica Bohemica},
keywords = {Fekete-Szegő problem; Sakaguchi function; uniformly starlike function; symmetric point; Fekete-Szegő problem; Sakaguchi function; uniformly starlike function; symmetric point},
language = {eng},
number = {3},
pages = {485-509},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points},
url = {http://eudml.org/doc/261977},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Yagmur, Nihat
AU - Orhan, Halit
TI - Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 3
SP - 485
EP - 509
AB - The authors obtain the Fekete-Szegő inequality (according to parameters $s$ and $t$ in the region $s^{2}+st+t^{2}<3$, $s\ne t$ and $s+t\ne 2$, or in the region $s^{2}+st+t^{2}>3,$$s\ne t$ and $s+t\ne 2$) 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 \lbrace \frac{(s-t)z ( D_{\lambda ,\mu }^{n}f(z))^{\prime }}{D_{\lambda ,\mu }^{n}f(sz)-D_{\lambda ,\mu }^{n}f(tz)}\bigg \rbrace >k \biggl \vert \frac{(s-t)z ( D_{\lambda ,\mu }^{n}f(z))^{\prime }}{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.
LA - eng
KW - Fekete-Szegő problem; Sakaguchi function; uniformly starlike function; symmetric point; Fekete-Szegő problem; Sakaguchi function; uniformly starlike function; symmetric point
UR - http://eudml.org/doc/261977
ER -

References

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