Uniqueness of admissible meromorphic functions in the unit disc

1999 ◽  
Vol 42 (4) ◽  
pp. 367-381 ◽  
Author(s):  
Mingliang Fang
Keyword(s):  
Unit Disc ◽  
Meromorphic Functions

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.

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.

scholarly journals Inclusion Relationships for Certain Subclasses of Meromorphic Functions Defined by Using the Extended Multiplier Transformations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
R. M. El-Ashwah
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Hadamard Product ◽  
Operator Inclusion ◽  
Inclusion Properties

Let denote the class of analytic functions in the punctured unit disc . Set , and define in terms of the Hadamard product by . In this paper, we introduce several new subclasses of analytic functions defined by means of the operator Inclusion properties of these classes and some applications involving integral operator are also considered.

scholarly journals The uniqueness problem for meromorphic functions in the unit disc sharing values and a set in an angular domain

2011 ◽  
Vol 109 (2) ◽  
pp. 240 ◽  
Author(s):  
Hong-Yan Xu ◽  
Cai-Feng Yi ◽  
Ting-Bin Cao
Keyword(s):  
Unit Disc ◽  
Meromorphic Functions ◽  
Shared Values ◽  
Uniqueness Problem ◽  
Angular Domain ◽  
Sharing Values

We investigate the uniqueness problem for meromorphic functions in the unit disc sharing four distinct values and one set in an angular domain, and obtain some relations between the Borel points and shared values of meromorphic functions in an angular domain. These results improve the theorem of Mao-Liu [10].

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