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

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.