scholarly journals Majorization for A Subclass of β-Spiral Functions of Order α Involving a Generalized Linear Operator

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Afaf A. Ali Abubaker ◽  
Maslina Darus ◽  
Daniel Breaz
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Class A

Motivated by Carlson-Shaffer linear operator, we define here a new generalized linear operator. Using this operator, we define a class of analytic functions in the unit disk U. For this class, a majorization problem of analytic functions is discussed.

scholarly journals Mapping properties for convolutions involving hypergeometric functions

2003 ◽  
Vol 2003 (17) ◽  
pp. 1083-1091 ◽  
Author(s):  
J. A Kim ◽  
K. H. Shon
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disk

Forμ≥0, we consider a linear operatorLμ:A→Adefined by the convolutionfμ∗f, wherefμ=(1−μ)z2F1(a,b,c;z)+μz(z2F1(a,b,c;z))′. Letφ∗(A,B)denote the class of normalized functionsfwhich are analytic in the open unit disk and satisfy the conditionzf′/f≺(1+Az)/1+Bz,−1≤A<B≤1, and letRη(β)denote the class of normalized analytic functionsffor which there exits a numberη∈(−π/2,π/2)such thatRe(eiη(f′(z)−β))>0,(β<1). The main object of this paper is to establish the connection betweenRη(β)andφ∗(A,B)involving the operatorLμ(f). Furthermore, we treat the convolutionI=∫0z(fμ(t)/t)dt ∗f(z)forf∈Rη(β).

scholarly journals Convolution properties of a class of bounded analytic functions

1992 ◽  
Vol 45 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Zou Zhongzhu ◽  
Shigeyoshi Owa
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Class A ◽  
Convolution Properties ◽  
Class Of Functions

Let A be the class of functions f(z) which are analytic in the unit disk U with f(0) = f′(0) - 1 = 0. A subclass S(λ, M) (λ > 0, M > 0) of A is introduced. The object of the present paper is to prove some interesting convolution properties of functions f(z) belonging to the class S(λ, M). Also a certain integral operator J for f(z) in the class A is considered.

scholarly journals On Differential Sandwich Theorems of Meromorphic Univalent Functions

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Waggas Galib Atshan ◽  
Rajaa Ali Hiress
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Meromorphic Univalent Functions

        By using of linear  operator, we obtain some Subordinations  and superordinations results for certain normalized meromorphic univalent analytic functions in the in the punctured open unit disk   Also we derive some sandwich theorems .

scholarly journals Some classes of p-valent analytic functions associated with hypergeometric functions

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1031-1038 ◽  
Author(s):  
Khalida Noor ◽  
Nasir Khan
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Class A ◽  
Radius Problem ◽  
Inclusion Results

We define a linear operator on the class A(p) of p-valent analytic functions in the open unit disc involving Gauss hypergeometric functions and introduce certain new subclasses of A(p) using this operator. Some inclusion results, a radius problem and several other interesting properties of these classes are studied.

scholarly journals New and Extended Results On Fourth-Order Differential Subordination for Univalent Analytic Functions

2020 ◽  
Vol 25 (2) ◽  
pp. 1-13 ◽  
Author(s):  
Waggas Galib Atshan ◽  
Ali Hussein Battor ◽  
Abeer Farhan Abaas ◽  
Georgia Irina Oros
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Fourth Order ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordination And Superordination

In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with linear operator for univalent analytic functions in open unit disk. Here, we extended some lemmas. Also  some interesting new results are obtained.

scholarly journals Generalized Briot-Bouquet Differential Equation Based on New Differential Operator with Complex Connections

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 42 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Rafida M. Elobaid ◽  
Suzan J. Obaiys
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Linear Operator ◽  
Differential Equations ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk

A class of Briot–Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit disk and generalize a class of Briot–Bouquet differential equations (BBDEs). We study and generalize new classes of analytic functions based on the new differential operator. Consequently, we define a linear operator with applications.

scholarly journals Class of Multivalent Analytic Functions Defined by a Linear Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
B. A. Frasin
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk

Making use of the linear operator defined in (Prajapat, 2012), we introduce the class of analytic and -valent functions in the open unit disk . Furthermore, we obtain some sufficient conditions for starlikeness and close-to-convexity and some angular properties for functions belonging to this class. Several corollaries and consequences of the main results are also considered.

scholarly journals On a Certain Subclass for Multivalent Analytic Functions with a Fixed Point Involving Linear Operator

2019 ◽  
pp. 515-526
Author(s):  
Asraa Abdul Jaleel Husien ◽  
Qassim Ali Shakir
Keyword(s):  
Fixed Point ◽  
Linear Operator ◽  
Integral Representation ◽  
Unit Disk ◽  
Analytic Functions ◽  
Extreme Points ◽  
Coefficient Estimates

In the present paper, we study a subclass for multivalent analytic functions with a fixed point w defined in the unit disk U involving linear operator. Also, we obtain coefficient estimates, extreme points, integral representation and radii of starlikeness and convexity.

scholarly journals Properties of some families of meromorphic multivalent functions involving certain linear operator

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 35-54 ◽  
Author(s):  
M.K. Aouf ◽  
B.A. Frasin
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Hadamard Products ◽  
Class A

Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce two novel subclasses ?a,c (p, A, B, ?) and ?+a,c (p, A, B, ?) of meromorphically multivalent functions. The main object of this paper is to investigate the various important properties and characteristics of those subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions. We also derive many results for the Hadamard products of functions belonging to the class ?+a,c (p, ?, ?, ?, ?).

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