scholarly journals Some Subordination Results onq-Analogue of Ruscheweyh Differential Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Huda Aldweby ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Differential Subordination

We derive theq-analogue of the well-known Ruscheweyh differential operator using the concept ofq-derivative. Here, we investigate several interesting properties of thisq-operator by making use of the method of differential subordination.

scholarly journals Starlikeness Condition for a New Differential-Integral Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 694 ◽  
Author(s):  
Mugur Acu ◽  
Gheorghe Oros
Keyword(s):  
Differential Operator ◽  
Integral Operator ◽  
Differential Subordination

A new differential-integral operator of the form I n f ( z ) = ( 1 − λ ) S n f ( z ) + λ L n f ( z ) , z ∈ U , f ∈ A , 0 ≤ λ ≤ 1 , n ∈ N is introduced in this paper, where S n is the Sălăgean differential operator and L n is the Alexander integral operator. Using this operator, a new integral operator is defined as: F ( z ) = β + γ z γ ∫ 0 z I n f ( z ) · t β + γ − 2 d t 1 β , where I n f ( z ) is the differential-integral operator given above. Using a differential subordination, we prove that the integral operator F ( z ) is starlike.

scholarly journals Differential Subordination Results for Holomorphic Functions Related to Differential Operator

2019 ◽  
Vol 11 (2) ◽  
pp. 46-53
Author(s):  
Abbas Kareem Wanas ◽  
S R Swamy
Keyword(s):  
Differential Operator ◽  
Integral Representation ◽  
Unit Disk ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties

,In the present work, we introduce and study a certain class of holomorphic functions defined by differential operator in the open unit disk . Also, we derive some important geometric properties for this class such as integral representation, inclusion relationship and argument estimate.

DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS

2013 ◽  
Vol 06 (04) ◽  
pp. 1350044
Author(s):  
Rabha M. El-Ashwash ◽  
Mohamed K. Aouf ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
New Class ◽  
Inclusion Properties

In this paper, a new class of analytic functions is introduced on the unit disk U which is defined by a certain differential operator. Some inclusion properties are discussed. Indeed, three other classes are also introduced and some differential subordination results are obtained.

scholarly journals Fractional differential superordination

2014 ◽  
Vol 45 (3) ◽  
pp. 275-284
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Fractional Order ◽  
Analytic Functions ◽  
Dual Problem ◽  
Differential Subordination ◽  
Geometric Properties ◽  
Differential Superordination ◽  
Fractional Differential ◽  
Admissible Functions

The notion of differential superordination was introduced by S.S. Miller and P.T. Mocanu as a dual concept of differential subordination. Recently, in Tamkang J. Math.[7], the author have introduced the notion of fractional differential subordination. In this work, we consider the dual problem of determining properties of analytic functions that satisfy the fractional differential superordination. By employing some types of admissible functions, involving differential operator of fractional order, we illustrate geometric properties such as starlikeness and convexity for a class of analytic functions in the unit disk. Moreover, applications are posed in the sequel.

scholarly journals Differential Sandwich Theorems for a Certain Class of Analytic Functions Defined by Differential Operator

2019 ◽  
pp. 209-220
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehai
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
First Order ◽  
Differential Subordination And Superordination

In this paper, we establish some applications of first order differential subordination and superordination results involving Hadamard product for a certain class of analytic functions with differential operator defined in the open unit disk. These results are applied to obtain sandwich results.

scholarly journals Third-Order Differential Subordination Results for Analytic Functions Associated with a Certain Differential Operator

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 99
Author(s):  
Amal Mohammed Darweesh ◽  
Waggas Galib Atshan ◽  
Ali Hussein Battor ◽  
Alina Alb Lupaş
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Maclaurin Series ◽  
Third Order ◽  
Differential Superordination ◽  
Admissible Functions

In this research, we study suitable classes of admissible functions and establish the properties of third-order differential subordination by making use a certain differential operator of analytic functions in U and have the normalized Taylor–Maclaurin series of the form: f(z)=z+∑n=2∞anzn, (z∈U). Some new results on differential subordination with some corollaries are obtained. These properties and results are symmetry to the properties of the differential superordination to form the sandwich theorems.

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