scholarly journals Two New Classes of Analytic Functions Defined by Strong Differential Subordinations and Superordinations

2019 ◽  
Vol 27 (2) ◽  
pp. 3-11
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Holomorphic Functions ◽  
Generalized Differential ◽  
Differential Subordinations

AbstractIn the present investigation, by making use of strong differential subordinations and superordinations, we introduce and study two new classes of holomorphic functions containing generalized differential operator. Also we determine important properties for functions belongs to these classes.

scholarly journals Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2487
Author(s):  
Alina Alb Lupaş ◽  
Georgia Oros
Keyword(s):  
Analytic Functions ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
New Approach ◽  
Ruscheweyh Derivative ◽  
Differential Superordination ◽  
Strong Differential Subordination ◽  
Extended Operator ◽  
Dual Notion ◽  
Differential Subordinations

The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯), f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

scholarly journals Some properties of a class of analytic functions involving a new generalized differential operator

2019 ◽  
Vol 38 (6) ◽  
pp. 33-42 ◽  
Author(s):  
A. A. Amourah ◽  
Feras Yousef
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Generalized Differential ◽  
Growth And Distortion Theorems

In the present paper, we introduce a new generalized differentialoperator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ defined on the openunit disc $U=\left\{ z\in%%TCIMACRO{\U{2102} }%%BeginExpansion\mathbb{C}:\left\vert z\right\vert <1\right\} $. A novel subclass $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ by means of the operator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ is also introduced. Coefficient estimates, growth and distortion theorems, closuretheorems, and class preserving integral operators for functions in the class $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ are discussed. Furthermore, sufficient conditions for close-to-convexity, starlikeness, and convexity for functions in the class $\Om are obtained

scholarly journals Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 174
Author(s):  
Matthew Olanrewaju Oluwayemi ◽  
Kaliappan Vijaya ◽  
Adriana Cătaş
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Closure Properties ◽  
Integral Means ◽  
Radius Of Starlikeness ◽  
Generalized Differential ◽  
The Relationship ◽  
Class Of Functions

In this article, we construct a new subclass of analytic functions involving a generalized differential operator and investigate certain properties including the radius of starlikeness, closure properties and integral means result for the class of analytic functions with negative coefficients. Further, the relationship between the results and some known results in literature are also established.

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.

scholarly journals Subclasses of Analytic Functions of Complex Order Involving Generalized Jackson's (p, q)-derivative

2021 ◽  
pp. 4819-4829
Author(s):  
A. Ta. Yousef ◽  
Z. Salleh
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Fractional Derivatives ◽  
Coefficient Estimates ◽  
Complex Order ◽  
Generalized Differential

This paper aims at introducing a new generalized differential operator and new subclass of analytic functions to obtain some interesting properties like coefficient estimates and fractional derivatives.

On a Generalization of Bounded Univalent Function of Complex Order

2018 ◽  
Vol 15 (2) ◽  
pp. 601-605
Author(s):  
C. Ramachandran ◽  
T. Soupramanien ◽  
J. Sokół
Keyword(s):  
Differential Operator ◽  
Univalent Function ◽  
Analytic Functions ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Coefficient Estimates ◽  
New Class ◽  
Complex Order ◽  
Generalized Differential

In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized differential operator Dnλ, μ.

scholarly journals The Application of Generalized Quasi-Hadamard Products of Certain Subclasses of Analytic Functions with Negative and Missing Coefficients

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 620
Author(s):  
En Ao ◽  
Shuhai Li
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Differential Operators ◽  
Closure Properties ◽  
Hadamard Products ◽  
Generalized Differential

In this paper, we introduce a new generalized differential operator using a new generalized quasi-Hadamard product, and certain new classes of analytic functions using subordination. We obtain certain results concerning the closure properties of the generalized quasi-Hadamard products and the generalized differential operators for this new subclasses of analytic functions with negative and missing coefficients.

scholarly journals Applications of Fractional Derivative on a Differential Subordinations and Superordinators for Analytic Functions Associated with Differential Operator

2021 ◽  
Vol 45 (03) ◽  
pp. 379-392
Author(s):  
ABBAS KAREEM WANAS ◽  
MASLINA DARUS
Keyword(s):  
Differential Operator ◽  
Fractional Derivative ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordinations

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

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