Certain classes of univalent functions with negative coefficients and $n$-starlike with respect to certain points

Abstract

In this paper we introduce three subclasses of $T$, $S_{s,n}^{\star}T(\alpha,\beta)$, $S_{c,n}^{\star}T(\alpha,\beta)$ and $S_{sc,n}^{\star}T(\alpha,\beta)$ consisting of analytic functions with negativecoefficients defined by using Salagean operator and are, respectively, $n$-starlike with respect to symmetric points, $n$-starlike with respect toconjugate points and $n$-starlike with respect to symmetric conjugate points. Several properties like, coefficient bounds, growth and distortiontheorems, radii of starlikeness, convexity and close-to-convexity are investigated.