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 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 Some properties of differential operator associated with generalized hypergeometric functions

2015 ◽  
Vol 46 (1) ◽  
pp. 75-83 ◽  
Author(s):  
Entisar El-yagubi ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Generalized Hypergeometric Functions ◽  
Generalized Derivative

In the present investigation, new subclasses of analytic functions in the open unit disk which are defined using generalized derivative operator are introduced. Several interesting properties of these classes are obtained.

scholarly journals A new criterion for close-to-convexity of partial sums of certain hypergeometric functions

1997 ◽  
Vol 10 (2) ◽  
pp. 197-202
Author(s):  
Massoud Jahangiri
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Criterion

We consider the partial sums of certain hypergeometric functions and establish conditions imposed on the locations of zeros of those polynomials in order to be close-to-convex in the open unit disk.

scholarly journals Partial sums of certain analytic functions

2001 ◽  
Vol 25 (12) ◽  
pp. 771-775 ◽  
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk

The object of the present paper is to consider the starlikeness and convexity of partial sums of certain analytic functions in the open unit disk.

scholarly journals The order of convexity for an integral operator

2016 ◽  
Vol 32 (1) ◽  
pp. 123-129
Author(s):  
VIRGIL PESCAR ◽  
◽  
CONSTANTIN LUCIAN ALDEA ◽  
◽  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Order Of Convexity

In this paper we consider an integral operator for analytic functions in the open unit disk and we derive the order of convexity for this integral operator, on certain classes of univalent functions.

scholarly journals Strong Differential Subordination Results for Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

2019 ◽  
pp. 159-168
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehdi
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Closed Unit Disk ◽  
Strong Differential Subordination

In this paper, by making use of the principle of strong subordination, we establish some interesting properties of multivalent analytic functions defined in the open unit disk and closed unit disk of the complex plane associated with Dziok-Srivastava operator.

scholarly journals On Certain Classes of Convex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Young Jae Sim ◽  
Oh Sang Kwon
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Real Numbers ◽  
Inverse Functions

For real numbersαandβsuch that0≤α<1<β, we denote by𝒦α,βthe class of normalized analytic functions which satisfy the following two sided-inequality:α<ℜ1+zf′′z/f′z<β  z∈𝕌,where𝕌denotes the open unit disk. We find some relationships involving functions in the class𝒦(α,β). And we estimate the bounds of coefficients and solve the Fekete-Szegö problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.

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