On the neighborhoods of certain subclasses of close-to-convex and quasi-convex

The neighborhoods of certain subclasses of close-to-convex and quasi-convex functions with respect to $k$-symmetric points are studied. If $f$ is in ${\mathcal S_{s,\ n}^{(k)}}[A, B]$ or ${\mathcal C_{s,\ n}^{(k)}}[A, B]$, some sufficient conditions are established such that all functions $g\in{\mathcal N_{\delta}}(f)$ are included in ${\mathcal S_{s,\ n}^{(k)}}[A, B]$ with this $\delta$ being the best possibility. Some of the results, presented in this paper, generalize and extend the corresponding results existing in some literatures.