scholarly journals Argument estimates of certain multivalent functions involving a linear operator

2002 ◽  
Vol 31 (11) ◽  
pp. 659-673 ◽  
Author(s):  
Nak Eun Cho ◽  
J. Patel ◽  
G. P. Mohapatra
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Open Unit ◽  
Open Unit Disk

The purpose of this paper is to derive some argument properties of certain multivalent functions in the open unit disk involving a linear operator. We also investigate their integral preserving property in a sector.

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 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 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 On a new linear operator formulated by Airy functions in the open unit disk

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Dumitru Baleanu
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Function Theory ◽  
Univalent Functions ◽  
Open Unit ◽  
Geometric Function Theory ◽  
Open Unit Disk ◽  
Airy Functions ◽  
Geometric Function ◽  
Difference Formula

AbstractIn this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk.

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 Certain Subclass of m -Valent Functions Associated with a New Extended Ruscheweyh Operator Related to Conic Domains

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Amnah E. Shammaky ◽  
Tamer M. Seoudy
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Geometric Properties

The main object of the present paper is to introduce certain subclass of m -valent functions associated with a new extended Ruscheweyh linear operator in the open unit disk. Also, we investigate a number of geometric properties including coefficient estimates and the Fekete–Szegö type inequalities for this subclass. Several known consequences of the main results are also pointed out.

scholarly journals On a class of meromorphicp-valent starlike functions involving certain linear operators

2002 ◽  
Vol 32 (5) ◽  
pp. 271-280 ◽  
Author(s):  
Jin-Lin Liu ◽  
Shigeyoshi Owa
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Starlike Functions ◽  
Linear Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Class Of Functions

Let∑pbe the class of functionsf(z)which are analytic in the punctured disk𝔼*={z∈ℂ:0<|z|<1}. Applying the linear operatorDn+pdefined by using the convolutions, the subclass𝒯n+p(α)of∑pis considered. The object of the present paper is to prove that𝒯n+p(α)⊂𝒯n+p−1(α). Since𝒯0(α)is the class of meromorphicp-valent starlike functions of orderα, all functions in𝒯n+p−1(α)are meromorphicp-valent starlike in the open unit disk𝔼. Further properties preserving integrals and convolution conditions are also considered.

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

Sign in / Sign up

Export Citation Format

Share Document