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Fixed coefficients for certain subclasses of starlike functions with negative coefficients

Aouf M., Al-Dohiman A.

Demonstratio Mathematica

2005

Vol. 38, nr 3

551--565

The main object of this paper is to study the class T*n,c(alfa,beta) of analytic functions with negative coefficients and with fixed second coefficients. Among other results of interest, we derive coefficient estimates, closure properties involving convex linear combinations, growth and distortion theorems, and radii of starlikeness and convexity for functions in the class T*n,c(alfa,beta). Many of these results are further extended to hold true for families of functions with finitely many fixed coefficients.