Abstract:
In this article, we consider classes $S_{s,\lambda}^*(p,\alpha,\beta)$, $S_{c,\lambda}^*(p,\alpha,\beta)$, and $S_{sc,\lambda}^*(p,\alpha,\beta)$ of p-valent analytic functions with negative coefficients in the unit disk. They are, respectively, $(\lambda,p)$-starlike with respect to symmetric points, $(\lambda,p)$-starlike with respect to conjugate points, and $(\lambda,p)$-starlike with respect to symmetric conjugate points. Necessary and sufficient coefficient conditions for functions $f$ belonging to these classes are obtained. Several properties such as the coefficient estimates, growth and distortion theorems, extreme points, radii of starlikeness, convexity, and integral operator are studied.
Keywords and phrases:p-valent functions, univalent functions, Salagean operator, starlike with respect to symmetric points.