Taiwanese Journal of Mathematics

CERTAIN CLASSES OF THE MEROMORPHIC HARMONIC FUNCTIONS WITH A POLE AT SOME FIXED POINT OF THE UNIT DISK

Metin Öztürk and Hakan Bostanci

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Abstract

The class $S_{H}(p)$, $0 \leq p \lt 1$, of complex valued, meromorphic harmonic univalent sense-preserving functions in the unit disk $U \backslash \{p\}$ is studied. The functions belong to $S_{H}(p)$ have the expansion $f(z) = \frac{\alpha}{z-p} + \sum_{n=0}^{\infty} c_{n} z^{n} + \overline{\sum_{n=1}^{\infty} d_{n} z^{n}} + A\log |z-p|$ and $\lim_{z \rightarrow p} f(z) = \infty$. Some coefficient estimates, distortion and area theorems are obtained. Sufficient coefficient conditions for a class of meromorphic harmonic univalent sense-preserving functions that are starlike and convex are given.

Article information

Source
Taiwanese J. Math., Volume 14, Number 4 (2010), 1417-1428.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405957

Digital Object Identifier
doi:10.11650/twjm/1500405957

Mathematical Reviews number (MathSciNet)
MR2663921

Zentralblatt MATH identifier
1213.30038

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C50: Coefficient problems for univalent and multivalent functions 30C55: General theory of univalent and multivalent functions

Keywords
harmonic meromorphic functions

Citation

Öztürk, Metin; Bostanci, Hakan. CERTAIN CLASSES OF THE MEROMORPHIC HARMONIC FUNCTIONS WITH A POLE AT SOME FIXED POINT OF THE UNIT DISK. Taiwanese J. Math. 14 (2010), no. 4, 1417--1428. doi:10.11650/twjm/1500405957. https://projecteuclid.org/euclid.twjm/1500405957


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