MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Some subclasses of close-to-convex and quasi-convex functions
Zhi-Gang Wang

Abstract

In the present paper, the author introduce two new subclasses ${\Cal S}_{sc}^{(k)}(\alpha,\beta,\gamma)$ of close-to-convex functions and ${\Cal C}_{sc}^{(k)}(\alpha,\beta,\gamma)$ of quasi-convex functions with respect to $2k$-symmetric conjugate points. The coefficient inequalities and integral representations for functions belonging to these classes are provided, the inclusion relationships and convolution conditions for these classes are also provided.

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Keywords: Close-to-convex functions, quasi-convex functions, differential subordination, Hadamard product, $2k$-symmetric conjugate points.

MSC: 30C45

Pages:  65--73     

Volume  59 ,  Issue  1$-$2 ,  2007