Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator

M. K. Aouf, et al. "Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 54.1 (2010): null. <http://eudml.org/doc/289833>.

@article{M2010,
abstract = {Let $A$ denote the class of analytic functions with the normalization $f(0)=f^\{\prime \}(0)-1=0$ in the open unit disc $U=\lbrace z:\left|z\right|<1\rbrace $.  Set \[f\_\{\lambda \}^\{n\}(z)=z+\sum \_\{k=2\}^\{\infty \}[1+\lambda (k-1)]^\{n\}z^\{k\}\quad (n\in N\_\{0\};\ \lambda \ge 0;\ z\in U),\] and define $f_\{\lambda ,\mu \}^\{n\}$ in terms of the Hadamard product \[f\_\{\lambda \}^\{n\}(z)\ast f\_\{\lambda ,\mu \}^\{n\}=\frac\{z\}\{(1-z)^\{\mu \}\}\quad (\mu >0;\ z\in U). \] In this paper, we introduce several subclasses of analytic functions defined by means of the operator $I_\{\lambda ,\mu \}^\{n\}:A\longrightarrow A$, given by \[ I\_\{\lambda ,\mu \}^\{n\}f(z)=f\_\{\lambda ,\mu \}^\{n\}(z)\ast f(z)\quad (f\in A;\ n\in N\_\{0;\}\ \lambda \ge 0;\ \mu >0). \] Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.},
author = {M. K. Aouf, A. Shamandy, A. O. Mostafa, S. M. Madian},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Analytic; Hadamard product; starlike; convex},
language = {eng},
number = {1},
pages = {null},
title = {Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator},
url = {http://eudml.org/doc/289833},
volume = {54},
year = {2010},
}

TY - JOUR
AU - M. K. Aouf
AU - A. Shamandy
AU - A. O. Mostafa
AU - S. M. Madian
TI - Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2010
VL - 54
IS - 1
SP - null
AB - Let $A$ denote the class of analytic functions with the normalization $f(0)=f^{\prime }(0)-1=0$ in the open unit disc $U=\lbrace z:\left|z\right|<1\rbrace $.  Set \[f_{\lambda }^{n}(z)=z+\sum _{k=2}^{\infty }[1+\lambda (k-1)]^{n}z^{k}\quad (n\in N_{0};\ \lambda \ge 0;\ z\in U),\] and define $f_{\lambda ,\mu }^{n}$ in terms of the Hadamard product \[f_{\lambda }^{n}(z)\ast f_{\lambda ,\mu }^{n}=\frac{z}{(1-z)^{\mu }}\quad (\mu >0;\ z\in U). \] In this paper, we introduce several subclasses of analytic functions defined by means of the operator $I_{\lambda ,\mu }^{n}:A\longrightarrow A$, given by \[ I_{\lambda ,\mu }^{n}f(z)=f_{\lambda ,\mu }^{n}(z)\ast f(z)\quad (f\in A;\ n\in N_{0;}\ \lambda \ge 0;\ \mu >0). \] Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.
LA - eng
KW - Analytic; Hadamard product; starlike; convex
UR - http://eudml.org/doc/289833
ER -