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

Annales Polonici Mathematici (1998)

- Volume: 69, Issue: 3, page 251-263
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.