International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 201-203

Meromorphic univalent function with negative coefficient

A. Dernek

Department of Mathematics, Marmara University, Göztepe Kampüsü, Istanbul 81080, Turkey

Received 20 September 1991

Copyright © 1994 A. Dernek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let Mn be the classes of regular functions f(z)=z1+a0+a1z+ defined in the annulus 0<|z|<1 and satisfying ReIn+1f(z)In+1f(z)>0, (n0), where I0f(z)=f(z), If(z)=(z1z(z1)2)f(z), Inf(z)=I(In1f(z)), and is the Hadamard convolution. We denote by Γn=MnΓ, where Γ denotes the class of functions of the form f(z)=z1+k=1|ak|zk. We obtained that relates the modulus of the coefficients to starlikeness for the classes Mn and Γn, and coefficient inequalities for the classes Γn.