On certain subclasses of multivalently meromorphic close-to-convex maps

@article{K1998,
abstract = {Let Mₚ denote the class of functions f of the form $f(z) = 1/z^p + ∑_\{k=0\}^∞ aₖz^k$, p a positive integer, in the unit disk E = |z| < 1, f being regular in 0 < |z| < 1. Let $L_\{n,p\}(α) = \{f: f ∈ Mₚ, Re\{-(z^\{p+1\}/p) (Dⁿf)^\{\prime \}\} > α\}$, α < 1, where $Dⁿf = (z^\{n+p\} f(z))^\{(n)\}/(z^p n!)$. Results on $L_\{n,p\}(α)$ are derived by proving more general results on differential subordination. These results reduce, by putting p =1, to the recent results of Al-Amiri and Mocanu.},
author = {K. S. Padmanabhan},
journal = {Annales Polonici Mathematici},
keywords = {meromorphic multivalently close-to-convex; differential subordination; convolution; meromorphic multivalently; subordination; close-to-convex meromorphic functions},
language = {eng},
number = {3},
pages = {251-263},
title = {On certain subclasses of multivalently meromorphic close-to-convex maps},
url = {http://eudml.org/doc/270452},
volume = {69},
year = {1998},
}

TY - JOUR
AU - K. S. Padmanabhan
TI - On certain subclasses of multivalently meromorphic close-to-convex maps
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 3
SP - 251
EP - 263
AB - Let Mₚ denote the class of functions f of the form $f(z) = 1/z^p + ∑_{k=0}^∞ aₖz^k$, p a positive integer, in the unit disk E = |z| < 1, f being regular in 0 < |z| < 1. Let $L_{n,p}(α) = {f: f ∈ Mₚ, Re{-(z^{p+1}/p) (Dⁿf)^{\prime }} > α}$, α < 1, where $Dⁿf = (z^{n+p} f(z))^{(n)}/(z^p n!)$. Results on $L_{n,p}(α)$ are derived by proving more general results on differential subordination. These results reduce, by putting p =1, to the recent results of Al-Amiri and Mocanu.
LA - eng
KW - meromorphic multivalently close-to-convex; differential subordination; convolution; meromorphic multivalently; subordination; close-to-convex meromorphic functions
UR - http://eudml.org/doc/270452
ER -