Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 18, No. 2, pp. 63-65 (2002)

Fekete-Szegő Functional for Non-Bazilevic Functions

N. Tuneski and M. Darus

Faculty of Mechanical Engineering, Skopje, University Kebangsaan Malaysia

Abstract: Let $f(z)=z+a_2z^2+a_3z^3+\cdots$ be an analytic function in the unit disk $\U$ and let the class of non-Bazilevic functions, for $0<\lambda<1$, be described with $\real\left\{f'(z)\left(z/f(z)\right)^{1+\lambda}\right\}>0,$ $z\in\U$. In this paper we obtain sharp upper bound of $|a_2|$ and of the Fekete-Szegö functional $|a_3-\mu a_2^2|$ for the class of non-Bazilevic functions and for some of its subclasses.

Keywords: non-Bazilevic function, Fekete-Szegő functional, sharp upper bound

Classification (MSC2000): 30C50

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