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

Abstract

In the present paper, the author introduce two new subclasses ${\text{CalS}}_{sc}^{(k)}(\alpha ,\beta ,\gamma )$ of close-to-convex functionsand ${\mathcal{C}}_{sc}^{(k)}(\alpha ,\beta ,\gamma )$ of quasi-convexfunctions with respect to $2k$-symmetric conjugate points. Thecoefficient inequalities and integral representations for functionsbelonging to these classes are provided, the inclusion relationshipsand convolution conditions for these classes are also provided.