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 00, (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.

Keywords

• univalent meromorphic functions
• Hadamard product.