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

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.