On certain subclasses of multivalently meromorphic close-to-convex maps
Annales Polonici Mathematici (1998)
- Volume: 69, Issue: 3, page 251-263
- ISSN: 0066-2216
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topK. S. Padmanabhan. "On certain subclasses of multivalently meromorphic close-to-convex maps." Annales Polonici Mathematici 69.3 (1998): 251-263. <http://eudml.org/doc/270452>.
@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 -
References
top- [1] H. Al-Amiri and P. T. Mocanu, On certain subclasses of meromorphic close-to-convex functions, Bull. Math. Soc. Sci. Math. Roumanie 38 (86) (1994), 3-15.
- [2] A. E. Livingston, Meromorphic multivalent close-to-convex functions, Trans. Amer. Math. Soc. 119 (1965), 167-177. Zbl0154.08103
- [3] S. S. Miller and P. T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289-305. Zbl0367.34005
- [4] S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 167-171. Zbl0439.30015
- [5] S. S. Miller and P. T. Mocanu, The theory and applications of second order differential subordinations, Studia Univ. Babeş-Bolyai Math. 34 (1989), 3-33. Zbl0900.30031
- [6] C. Pommerenke, Univalent functions, Vandenhoeck and Ruprecht, Göttingen, 1975.
- [7] S. Ruscheweyh, Eine Invarianzeigenschaft der Basilevič-Funktionen, Math. Z. 134 (1973), 215-219.
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