Certain subclasses of close-to-convex and quasi-convex functions with respect to $k$-symmetric points

Zh.-G. Wang

Changsha University of Science and Technology

Abstract: In the present paper, the author introduce two new subclasses $\mathcal C^{(k)}(\alpha,\beta,\gamma)$ of close-to-convex functions and $\mathcal QC^{(k)}(\alpha,\beta,\gamma)$ of quasi-convex functions with respect to $k$-symmetric points. The sufficient conditions and integral representations for functions belonging to these classes are provided, the inclusion relationships and convolution conditions for these classes are also provided.

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

Submitted by: F. G. Avkhadiev
Received: 16.03.2006

Language: English

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