Some generalizations of the class of analytic functions with respect to k-symmetric points

Abstract

In this article, we introduce a new class $M_{s}^{k}[\alpha,\beta,\lambda]$ which generalizes the various classes of analytic functions with respect to k-symmetric points. Naturally, the class $M_{s}^{k}[\alpha,\beta,\lambda]$ combines the classes $S_{s}^{k}(\alpha,\beta)$ and $C_{s}^{k}(\alpha,\beta)$. We also study the coefficient estimates and obtain some inequalities related to the coefficients of functions in these classes. We develop the integral representation, inclusions and convolution conditions for the functions in the class $M_{s}^{k}[\alpha,\beta,\lambda]$ .