Let f be a function meromorphic on the open unit disk D, with angular boundary limits bounded by one in modulus almost everywhere on the unit circle. We give sufficient conditions in terms of boundary asymptotics at finitely many points on the unit circle T for f to be a ratio of two finite Blaschke products. A necessary condition is that f has finitely many poles in D, i.e., that f is a genera...

We study a class of functions A given by Epstein in Towers of finite type complex analytic maps, ProQuest LLC, Ann Arbor, MI, 1993, called finite-type maps. We extend a result related with the Julia set given by Baker, Domı́nguez in Some connectedness properties of Julia sets, Complex Variable Theory Appl. 41 (2000), 371–389, and Baker, Domı́nguez, and Herring in Dynamics of functions meromorphic...

In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + ḡ using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for this family of meromorphic harmonic functions are obtained. Keywords—Harmonic mappings, Meromorphic fu...

We introduce and investigate two new subclasses ℳ σ (α, λ) and ℳ σ (β, λ) of meromorphic bi-univalent functions defined on Δ = {z : z ∈ ℂ, 1 < |z | <∞}. For functions belonging to these classes, estimates on the initial coefficients are obtained.

In this paper, we introduce two subclasses Ωp(α) and Λ ∗ p(α) of meromorphic pvalent functions in the punctured diskD = {z : 0 < |z| < 1}. Coefficient inequalities, distortion theorems, the radii of starlikeness and convexity, closure theorems and Hadamard product ( or convolution) of functions belonging to these classes are obtained.