Coefficient Inequalities for Certain Classes of Meromorphically Starlike and Meromorphically Convex Functions

Volume 4, Issue 1, 2003

Article 17

COEFFICIENT INEQUALITIES FOR CERTAIN CLASSES OF MEROMORPHICALLY STARLIKE AND MEROMORPHICALLY CONVEX FUNCTIONS

SHIGEYOSHI OWA AND NICOLAE N. PASCU

DEPARTMENT OF MATHEMATICS
KINKI UNIVERSITY
HIGASHI-OSAKA, OSAKA 577-8502
JAPAN.
E-Mail: owa@math.kindai.ac.jp

DEPARTMENT OF MATHEMATICS
TRANSILVANIA UNIVERSITY OF BRASOV
R-2200 BRASOV
ROMANIA.
E-Mail: pascu@info.unitbv.ro

Received 27 November, 2002; Accepted 17 January, 2003.
Communicated by: H.M. Srivastava

ABSTRACT. Let $\Sigma _{r}$ be the class of meromorphic functions

in $\mathbb{D}%% _{r}$ with a simple pole at the origin. Two subclasses $T_{r}^{\ast }(\alpha )$ and $\mathcal{C}_{r}(\alpha )$ of $\Sigma _{r}$ are considered. Some coefficient properties of functions

to be in the classes $T_{r}^{\ast }(\alpha )$ and $\mathcal{C}_{r}(\alpha )$ of $\Sigma _{r}$ are discussed. Also, the starlikeness and the convexity of functions

in $\Sigma _{r}$ are discussed.

Key words:
Meromorphic functions, Univalent functions, Starlike functions, Convex functions.

2000 Mathematics Subject Classification:
Primary 30C45.

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