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Sharpness results of certain class of analytic functions
by P. Vasundhra

Vol. 5 No. 1 (2010) P.11~P.24

ABSTRACT

The main aim of this paper is to use the concept of finite Blaschke product to prove sharpness of some of the known results. Geometric properties of a class of functions $\mathcal{U}(\lambda)$ were discussed in [8, 11, 12]. Also, starlikeness of $\mathcal{U}(\lambda,\mu) \cap \ \mathcal{A}_n$ for $\mu \le n$ was obtained in [9, 10]. In this paper, we prove the sharpness of those results using the technique of R. Fournier [3] which was later revised by R. Fournier and S. Ponnusamy [5].

KEYWORDS
starlikeness, strongly starlikeness, finite Blaschke product

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 30C45

MILESTONES

Received: 2008-07-29
Revised : 2008-09-16
Accepted: 2008-09-16

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