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  Volume 9, Issue 2, Article 32
Sufficient Conditions for Starlikeness and Convexity in $|z|< 1/2$

    Authors: Mamoru Nunokawa, Shigeyoshi Owa, Yayoi Nakamura, Toshio Hayami,  
    Keywords: Analytic, Starlike, Convex.  
    Date Received: 18/02/08  
    Date Accepted: 04/06/08  
    Subject Codes:

Primary 30C45.

    Editors: Anthony Sofo,  

For analytic functions $ f(z)$ with $ f(0) = f^{prime}(0)-1=0$ in the open unit disc $ mathbb{E}$, T. H. MacGregor has considered some conditions for $ f(z)$ to be starlike or convex. The object of the present paper is to discuss some interesting problems for $ f(z)$ to be starlike or convex for $ vert zvert < frac{1}{2}$.

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