On subclasses of close-to-convex and quasi-convex functions with respect to $2k$-symmetric conjugate points

In the present paper, the authors introduce two new subclasses $\mathcal S_{sc}^{(k)}(\lambda,\alpha)$ of close-to-convex functions and $\mathcal C_{sc}^{(k)}(\lambda,\alpha)$ of quasi-convex functions with respect to $2k$-symmetric conjugate points. The integral representations and convolution conditions for these classes are provided. Some coefficient inequalities for functions belonging to these classes and their subclasses with negative coefficients are also provided.