ON A SUBCLASS OFCERTAIN STARLIKE FUNCTIONS WITH NEGATIVE COEFFICIENTS

Abstract

 This work presents the class of functions, note by P(n,l,a), which contain univalent functions with negative coefficients, satisfying: Re{(zf'(z)+lz²f''(z))/(lzf'(z)+(1-l)f(z))}>a. If f_j(z)ÎP(n,l,a), j=1,m, then the convolution of theese functions, h(z), lies to the class P(n,l,b), where we have b.The author obtain the order of starlikeness of a convex function of order a, with negative coefficients. The theorems 2, 3, 4 and corrolaris 1, 2, 4, 5 are original results of the author.