MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
A class of univalent functions defined by using Hadamard product
M. K. Aouf, H. M. Hossen, A. Y. Lashin

Abstract

In this paper we introduce the class $L_{\alpha}^*(\lambda,\beta)$ of functions defined by $f*S_{\alpha}(z)$ of $f(z)$ and $S_{\alpha}=\dfrac z{(1-z)^{2(1-\alpha)}}$. We determine coefficient estimates, closure theorems, distortion theorems and radii of close-to-convexity, starlikeness and convexity. Also we find integral operators and some results for Hadamard products of functions in the class $L_{\alpha}^*(\lambda,\beta)$. Finally, in terms of the operators of fractional calculus, we derive several sharp results depicting the growth and distortion properties of functions belonging to the class $L_{\alpha}^*(\lambda,\beta)$.

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Keywords: Univalent functions, Hadamard product, fractional calculus.

MSC: 30C45

Pages:  83--96     

Volume  55 ,  Issue  3$-$4 ,  2003