Fixed coefficients for certain class of analytic functions with negative coefficients

Abstract

In this paper we consider the class $T_p (n,alpha)$ consisting of analytic and univalent functions with negative coefficients and with fixed second coefficient. The object of the present paper is to show coefficient estimates, convex linear combinations, some distortion theorems and radius of convexity for f(z) in the class $T_p (n,alpha)$. The results are generalized to families with finetely many fixed coefficients.