Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 1, pp. 31-37 (2004)

Starlike and convex functions with respect to conjugate points

V. Ravichandran

Sri Venkateswara College of Engineering, India

Abstract: An analytic functions $f(z)$ defined on $\UD = \{z: |z| < 1\}$ and normalized by $f(0)=0$, $f'(0)=1$ is starlike with respect to conjugate points if $\repart\left\{\frac{zf'(z)}{f(z)+\overline{f}(\overline{z})} \right\} > 0, z \in \UD$. We obtain some convolution conditions, growth and distortion estimates of functions in this and related classes.

Keywords: Convex functions, starlike functions, conjugate points.

Classification (MSC2000): 30C45

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