Some subclasses of close-to-convex and quasi-convex functions

Zhi-Gang Wang

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.