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 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.

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

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

scholarly journals Coefficient estimates for certain subclasses of spiral-like functions of complex order

2010 ◽  
Vol 23 (7) ◽  
pp. 763-768 ◽  
Author(s):  
H.M. Srivastava ◽  
Qing-Hua Xu ◽  
Guang-Ping Wu
Keyword(s):  
Coefficient Estimates ◽  
Complex Order

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 Coefficients estimates for functions inBn(α)

2003 ◽  
Vol 2003 (59) ◽  
pp. 3761-3767 ◽  
Author(s):  
S. Abdul Halim
Keyword(s):  
Differential Operator ◽  
Unit Disc ◽  
Coefficient Estimates ◽  
Class Of Functions

We consider functionsf, analytic in the unit disc and of the normalised formf(z)=z+∑k=2∞akzk. For functionsf∈Bn(α), the class of functions involving the Sălăgean differential operator, we give some coefficient estimates, namely,|a2|,|a3|, and|a4|.

scholarly journals Research on Geometric Mappings in Complex Systems Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Yanyan Cui ◽  
Chaojun Wang ◽  
Sifeng Zhu
Keyword(s):  
Banach Spaces ◽  
Systems Analysis ◽  
Starlike Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Reinhardt Domains ◽  
Complex Order ◽  
Starlike Mappings

We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order λ, in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order λ. By the properties of functions with positive real parts and considering the zero of order k, we obtain the coefficient estimates for almost starlike functions of complex order λ on D. We also discuss the invariance of almost starlike mappings of complex order λ on Reinhardt domains and on the unit ball B in complex Banach spaces. The conclusions contain and generalize some known results.

scholarly journals Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

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]).

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