On the boundary properties and the spherical derivatives of meromorphic functions in the unit disc

1973 ◽  
Vol 132 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Hidenobu Yoshida
Keyword(s):  
Unit Disc ◽  
Meromorphic Functions ◽  
Boundary Properties ◽  
Derivatives Of

Derivatives of Meromorphic Functions with Multiple Zeros and Rational Functions

2007 ◽  
Vol 8 (2) ◽  
pp. 483-491 ◽  
Author(s):  
Xuecheng Pang ◽  
Shahar Nevo ◽  
Lawrence Zalcman
Keyword(s):  
Meromorphic Functions ◽  
Rational Functions ◽  
Multiple Zeros ◽  
Derivatives Of

scholarly journals A Criterion for Normalcy

1968 ◽  
Vol 32 ◽  
pp. 277-282 ◽  
Author(s):  
Paul Gauthier
Keyword(s):  
Meromorphic Function ◽  
Holomorphic Function ◽  
Unit Disc ◽  
Meromorphic Functions

Gavrilov [2] has shown that a holomorphic function f(z) in the unit disc |z|<1 is normal, in the sense of Lehto and Virtanen [5, p. 86], if and only if f(z) does not possess a sequence of ρ-points in the sense of Lange [4]. Gavrilov has also obtained an analagous result for meromorphic functions by introducing the property that a meromorphic function in the unit disc have a sequence of P-points. He has shown that a meromorphic function in the unit disc is normal if and only if it does not possess a sequence of P-points.

On the behaviour of the successive derivatives of meromorphic functions on the final set

2013 ◽  
Vol 120 (1) ◽  
pp. 131-149
Author(s):  
Thierry Meyrath ◽  
Jürgen Müller
Keyword(s):  
Meromorphic Functions ◽  
Derivatives Of

Defective functions of meromorphic functions in the unit disc

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Ewa Ciechanowicz
Keyword(s):  
Unit Disc ◽  
Meromorphic Functions

AbstractLet

scholarly journals Fourier coefficients of meromorphic functions in the unit disc

2021 ◽  
Author(s):  
Константин Малютин ◽  
Алена Наумова
Keyword(s):  
Unit Disc ◽  
Fourier Coefficients ◽  
Meromorphic Functions

Multivalent and Meromorphic Functions of Bounded Boundary Rotation

1975 ◽  
Vol 27 (1) ◽  
pp. 186-199 ◽  
Author(s):  
Ronald J. Leach
Keyword(s):  
Critical Points ◽  
Analytic Functions ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

The classVk(p). We generalize the class Vk of analytic functions of bounded boundary rotation [8] by allowing critical points in the unit disc U.Definition. Let f(z) = aqzq + . . . (q 1) be analytic in U. Then f(z) belongs to the class Vk(p) if for r sufficiently close to 1,andWe note that (1.1) implies that / has precisely p — 1 critical points in U.

scholarly journals On Metric Properties of Sets of Angular Limits of Meromorphic Functions

1966 ◽  
Vol 26 ◽  
pp. 121-126 ◽  
Author(s):  
J. E. Mcmillan
Keyword(s):  
Harmonic Measure ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Linear Measure ◽  
Closed Set ◽  
Angular Limit ◽  
Metric Properties ◽  
Angular Limits

Let f be a nonconstant function meromorphic in the unit disc , with circumference C, and let Ez be a subset of C with positive (linear) measure. Suppose that at each ζ ∈ Ezf has an angular limit aζ and let It is known that Ew contains a closed set with positive harmonic measure (see Priwalow [6, p. 210] or Tsuji [7, p. 339]).

scholarly journals Convolution Properties for Some Subclasses of Meromorphic Functions of Complex Order

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa ◽  
H. M. Zayed
Keyword(s):  
Unit Disc ◽  
Meromorphic Functions ◽  
Coefficient Estimates ◽  
Complex Order ◽  
Convolution Properties

Making use of the operatorLυfor functions of the formfz=1/z+∑k=1∞akzk-1, which are analytic in the punctured unit discU∗={z:z∈Cand0<|z|<1}=U∖{0}, we introduce two subclasses of meromorphic functions and investigate convolution properties, coefficient estimates, and containment properties for these subclasses.

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