A CERTAIN FRACTIONAL DERIVATIVE OPERATOR AND ITS APPLICATIONS TO A NEW CLASS OF ANALYTIC AND MULTIVALENT-FUNCTIONS WITH NEGATIVE COEFFICIENTS .2.

Recently, the authors made use of a certain operator of fractional der ivatives in order to introduce (and initiate a systematic study of) a novel subclass T-p(alpha, beta, lambda) of analytic and p-valent funct ions with negative coefficients. In this sequel to the aforementioned work, they prove a number of closure and inclusion theorems and determ ine the radii of p-valently close-to-convexity, starlikeness, and conv exity for the class T-p(alpha, beta, lambda). They also obtain a class -preserving integral operator of the form: F(z)= (J(gamma,p)f)(z):= ga mma+p/z(gamma) integral(0)(z) t(gamma-1) f(t) dt (gamma > -p) for the class studied here. (C) 1995 Academic Press, Inc.