scholarly journals A Class of p-valent Functions Defined by Differential Operator

2021 ◽  
Vol 2 (18) ◽  
pp. 60-76
Author(s):  
Salma Faraj Ramadan ◽  
Keyword(s):  
Differential Operator ◽  
Integral Representation ◽  
Analytic Functions ◽  
Arithmetic Mean ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk ◽  
Inclusion Properties ◽  
Class A

In the present paper, we introduce the class A of p-valent analytic functions in the open unit disk We investigate some inclusion properties, coefficient bounds, distortion theorem, -neighborhoods and partial sums. Also we obtain integral representation, weighted and arithmetic mean.

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 SOME INCLUSION PROPERTIES FOR CERTAIN K-UNIFORMLY SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH WRIGHT FUNCTION

2019 ◽  
Vol 7 (9) ◽  
pp. 218-229
Author(s):  
E. E. Ali
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Integral Operators ◽  
Special Property ◽  
Open Unit ◽  
Open Unit Disk ◽  
Wright Function ◽  
Inclusion Properties

A new operator  is introduced for functions of the form   which are analytic in the open unit disk . We introduce several inclusion properties of the new k-uniformly classes , ,    and    of analytic functions defined by using the Wright function with the operator    and the main object of this paper is to investigate various inclusion relationships for these classes. In addition, we proved that a special property is preserved by some integral operators.

scholarly journals Fractional heat equation optimized by a chaotic function

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 173-178
Author(s):  
Rabha Ibrahim ◽  
Mayada Wazi ◽  
Dumitru Baleanu ◽  
Nadia Al-Saidi
Keyword(s):  
Differential Operator ◽  
Heat Equation ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Fractional Heat Equation ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Extended Operator

In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.

scholarly journals A New Parametric Differential Operator of p-Valently Analytic Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Samir B. Hadid ◽  
Rabha W. Ibrahim ◽  
G. Murugusundaramoorthy
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties

Newly, numerous investigations are considered utilizing the idea of parametric operators (integral and differential). The objective of this effort is to formulate a new 2D-parameter differential operator (PDO) of a class of multivalent functions in the open unit disk. Consequently, we formulate the suggested operator in some interesting classes of analytic functions to study its geometric properties. The recognized class contains some recent works.

scholarly journals Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 783 ◽  
Author(s):  
Ibtisam Aldawish ◽  
Tariq Al-Hawary ◽  
B. A. Frasin
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Open Unit Disc ◽  
Class A ◽  
Class Of Functions

Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

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.

scholarly journals Sandwich Theorems for Multivalent Analytic Functions Associated with Differential Operator

2021 ◽  
Vol 45 (01) ◽  
pp. 7-20
Author(s):  
ABBAS KAREEM WANAS ◽  
ALB LUPAŞ ALINA
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk

The purpose of this paper is to derive subordination and superordination results involving differential operator for multivalent analytic functions in the open unit disk. These results are applied to obtain sandwich results. Our results extend corresponding previously known results.

scholarly journals Symmetric Conformable Fractional Derivative of Complex Variables

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 363 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Rafida M. Elobaid ◽  
Suzan J. Obaiys
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Unit Disk ◽  
Analytic Functions ◽  
Differential Operators ◽  
Function Theory ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Symmetric Differential Operators

It is well known that the conformable and the symmetric differential operators have formulas in terms of the first derivative. In this document, we combine the two definitions to get the symmetric conformable derivative operator (SCDO). The purpose of this effort is to provide a study of SCDO connected with the geometric function theory. These differential operators indicate a generalization of well known differential operator including the Sàlàgean differential operator. Our contribution is to impose two classes of symmetric differential operators in the open unit disk and to describe the further development of these operators by introducing convex linear symmetric operators. In addition, by acting these SCDOs on the class of univalent functions, we display a set of sub-classes of analytic functions having geometric representation, such as starlikeness and convexity properties. Investigations in this direction lead to some applications in the univalent function theory of well known formulas, by defining and studying some sub-classes of analytic functions type Janowski function and convolution structures. Moreover, by using the SCDO, we introduce a generalized class of Briot–Bouquet differential equations to introduce, what is called the symmetric conformable Briot–Bouquet differential equations. We shall show that the upper bound of this class is symmetric in the open unit disk.

scholarly journals Study on subclasses of analytic functions

2017 ◽  
Vol 9 (1) ◽  
pp. 122-139 ◽  
Author(s):  
Imran Faisal ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Conjugate Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Convolution Properties

AbstractBy making use of new linear fractional differential operator, we introduce and study certain subclasses of analytic functions associated with Symmetric Conjugate Points and defined in the open unit disk 𝕌 = {z : |z| < 1}. Inclusion relationships are established and convolution properties of functions in these subclasses are discussed.

scholarly journals Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

2020 ◽  
Vol 28 (1) ◽  
pp. 105-114
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Generalized Operator ◽  
Generalized Differential

AbstractInequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

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