scholarly journals On Angular Limits of Normal Meromorphic Functions: A Geometric Aspect

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zarko Pavicevic
Keyword(s):  
Meromorphic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Geometric Aspect ◽  
Limit Values ◽  
Angular Limit ◽  
Normal Meromorphic Function ◽  
Lindelöf Theorem ◽  
Necessary And Sufficient ◽  
Angular Limits

We will prove the assertions which give necessary and sufficient conditions for a normal meromorphic function on the open unit disk to have an angular limit. The results obtained show that the conditions from the classical Lindelöf theorem, as well as the theorems of Lehto and Virtanen and Bagemihl and Seidel, concerning angular limit values of meromorphic functions, can be weakened.

Radial and Angular Limits of Meromorphic Functions

1963 ◽  
Vol 15 ◽  
pp. 471-474 ◽  
Author(s):  
G. T. Cargo
Keyword(s):  
Meromorphic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Classical Theorem ◽  
Radial Limit ◽  
Angular Limit ◽  
Normal Functions ◽  
Bounded Holomorphic Function ◽  
Bounded Holomorphic ◽  
Angular Limits

Let us say that a function denned in the open unit disk D has the Montel property if the set of those points eiθ on the unit circle C where the radial limit exists coincides with the set where the angular limit exists. By a classical theorem of Montel (4), every bounded holomorphic function has this property. Meromorphic functions omitting at least three values and, more generally, the normal functions recently introduced by Lehto and Virtanen (3) also enjoy the Montel property (also see 1).

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 On Fully-Convex Harmonic Functions and their Extension

2018 ◽  
Vol 38 (2) ◽  
pp. 51-60
Author(s):  
Shahpour Nosrati ◽  
Ahmad Zireh
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Circular Arc ◽  
Coefficient Condition ◽  
Necessary And Sufficient ◽  
Convex Univalent Functions

‎Uniformly convex univalent functions that introduced by Goodman‎, ‎maps every circular arc contained in the open unit disk with center in it into a convex curve‎. ‎On the other hand‎, ‎a fully-convex harmonic function‎, ‎maps each subdisk $|z|=r<1$ onto a convex curve‎. ‎Here we synthesis these two ideas and introduce a family of univalent harmonic functions which are fully-convex and uniformly convex also‎. ‎In the following we will mention some examples of this subclass and obtain a necessary and sufficient conditions and finally a coefficient condition will attain with convolution‎.

scholarly journals Applications of Borel Distribution Series on Analytic Functions

2020 ◽  
pp. 71-82
Author(s):  
Abbas Kareem Wanas ◽  
Jubran Abdulameer Khuttar
Keyword(s):  
Power Series ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sigma Delta ◽  
The Family ◽  
Necessary And Sufficient

The purpose of the present paper is to determine the necessary and sufficient conditions for the power series B_{\mu} whose coefficients are probabilities of the Borel distribution to be in the family H(\lambda, \sigma, \delta, \mu) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral representation, radii of starlikeness and convexity. Also we discuss the extreme points and neighborhood property for functions belongs to this family.

scholarly journals Some new harmonic mappings convex in one direction and their convolution

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6131-6139
Author(s):  
Chinu Singla ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Unit Disc ◽  
Sufficient Conditions ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc ◽  
Hadamard Products ◽  
New Family ◽  
Convex In One Direction ◽  
A New Technique ◽  
Necessary And Sufficient

In the present article, we construct a new family of locally univalent and sense preserving harmonic mappings by considering a suitable transformation of normalized univalent analytic functions defined in the open unit disc D. We present necessary and sufficient conditions for the functions of this new family to be univalent. Apart from studying properties of this new family, results about the convolutions or Hadamard products of functions from this family with some suitable analytic or harmonic mappings are proved by introducing a new technique which can also be used to simplify the proofs of earlier known results on convolutions of harmonic mappings. The technique presented also enables us to generalize existing such results.

scholarly journals Simple sufficient conditions for starlikeness and convexity for meromorphic functions

2016 ◽  
Vol 14 (1) ◽  
pp. 557-566
Author(s):  
Pranay Goswami ◽  
Teodor Bulboacă ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Unit Disk ◽  
Meromorphic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases ◽  
Convexity Conditions

AbstractIn this paper we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.

scholarly journals Analytic functions over valued fields

1990 ◽  
Vol 13 (2) ◽  
pp. 247-252
Author(s):  
R. Bhaskaran ◽  
V. Karunakaran
Keyword(s):  
Unit Ball ◽  
Fixed Points ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Ball ◽  
Valued Fields ◽  
Complete Field ◽  
Necessary And Sufficient

LetKbe a non-archimedean, non-trivially (rank 1) valued complete field.B,B0denote the closed and open unit ball ofKrespectively. Necessary and sufficient conditions for analytic functions defined onB,B0with values inKto be injective, necessary and sufficient conditions for fixed points, the problem of subordination are studied in this paper.

scholarly journals A Subclass of q-Starlike Functions Defined by Using a Symmetric q-Derivative Operator and Related with Generalized Symmetric Conic Domains

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 917
Author(s):  
Shahid Khan ◽  
Saqib Hussain ◽  
Muhammad Naeem ◽  
Maslina Darus ◽  
Akhter Rasheed
Keyword(s):  
Unit Disk ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Necessary And Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Structural Formulas ◽  
Necessary And Sufficient

In this paper, the concepts of symmetric q-calculus and conic regions are used to define a new domain Ωk,q,α˜, which generalizes the symmetric conic domains. By using the domain Ωk,q,α˜, we define a new subclass of analytic and q-starlike functions in the open unit disk U and establish some new results for functions of this class. We also investigate a number of useful properties and characteristics of this subclass, such as coefficients estimates, structural formulas, distortion inequalities, necessary and sufficient conditions, closure and subordination results. The proposed approach is also compared with some existing methods to show the reliability and effectiveness of the proposed methods.

scholarly journals Non-Weakly Supercyclic Weighted Composition Operators

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Z. Kamali ◽  
K. Hedayatian ◽  
B. Khani Robati
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disc ◽  
Space Of Analytic Functions ◽  
Weighted Composition ◽  
Necessary And Sufficient

We give sufficient conditions under which a weighted composition operator on a Hilbert space of analytic functions is not weakly supercyclic. Also, we give some necessary and sufficient conditions for hypercyclicity and supercyclicity of weighted composition operators on the space of analytic functions on the open unit disc.

scholarly journals Applications of Beta Negative Binomial Distribution Series on Holomorphic Functions

2021 ◽  
pp. 271-292
Author(s):  
Abbas Kareem Wanas ◽  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Power Series ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Necessary And Sufficient

The purpose of this article is to derive the necessary and sufficient conditions for the power series 〖P℘〗_(ℷ,γ)^μ (t) whose coefficients are probabilities of the beta negative binomial distribution to be in the family F(σ,τ,ϵ,η,μ,ℷ,γ) of holomorphic functions which are defined in the open unit disk. We establish a number of important geometric properties, such as, coefficient estimates, extreme points, neighborhood property, integral representation, radii of starlikeness and convexity and Hadamard product properties for functions belongs to this family. Also we determinate some differential subordination properties of the power series 〖P℘〗_(ℷ,γ)^μ (t).

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