International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 201-203
doi:10.1155/S0161171294000293
Meromorphic univalent function with negative coefficient
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.
Abstract
Let Mn be the classes of regular functions f(z)=z−1+a0+a1z+… defined in the annulus 0<|z|<1 and satisfying ReIn+1f(z)In+1f(z)>0, (n∈ℕ0), where I0f(z)=f(z), If(z)=(z−1−z(z−1)−2)∗f(z), Inf(z)=I(In−1f(z)), and ∗ is the Hadamard convolution. We denote by Γn=Mn⋃Γ, where Γ denotes the class of functions of the form f(z)=z−1+∑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.