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 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.

Some properties for certain subclasses of analytic functions defined by a general differential operator

2019 ◽  
Vol 13 (07) ◽  
pp. 2050134
Author(s):  
Erhan Deniz ◽  
Murat Çağlar ◽  
Yücel Özkan
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Partial Sums ◽  
Integral Means

In this paper, we study two new subclasses [Formula: see text] and [Formula: see text] of analytic functions which are defined by means of a differential operator. Some results connected to partial sums and neighborhoods and integral means related to these subclasses are obtained.

scholarly journals Integral means of certain class of analytic functions

1993 ◽  
Vol 16 (3) ◽  
pp. 459-464
Author(s):  
Gao Chunyi
Keyword(s):  
Analytic Functions ◽  
Starlike Function ◽  
Integral Means ◽  
Alpha Beta ◽  
Class Of Functions ◽  
Extremal Properties

In this paper we discuss the following class of functionsSλ(α,β)={f(z):|f(z)g(z)−1|<β|λf(z)g(z)+1|,z∈D}  where  0≤λ≤1,0<β≤1,0≤α<1, andf(z)=z+∑n=2∞anznis analytic inD={z:|z|<1},g(z)is a starlike function of orderα. A subordination about this class is obtained, the integral means of functions inSλ(α,β)and some extremal properties are studied.

scholarly journals A subordination results for a class of analytic functions defined by q-differential operator

2020 ◽  
Vol 19 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Basem Aref Frasin ◽  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Means

AbstractIn this paper, we derive several subordination results and integral means result for certain class of analytic functions defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered.

scholarly journals Subordination results for a class of analytic functions

2021 ◽  
Vol 7 (1) ◽  
pp. 30-42
Author(s):  
M. K. Aouf ◽  
B. A. Frasin ◽  
G. Murugusundaramoorthy
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Means ◽  
Complex Order

AbstractIn this paper, we derive several subordination results and integral means result for certain class of analytic functions with complex order defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered

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 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 On analytic functions with reference to an integral operator

1983 ◽  
Vol 28 (2) ◽  
pp. 207-215 ◽  
Author(s):  
R. Parvatham ◽  
T.N. Shanmugam
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Sharp Estimate ◽  
Radius Of Starlikeness ◽  
Image Position ◽  
Class Of Functions

Let E = {z: |z| < 1} and let H = {w : regular in E, w(0) = 0, |w(z)| < l, z ∈ E}.Let P(A, B) denote the class of functions in E which can be put in the form (1 + Aw(z))/(1 + Bw(z)), −1 ≤ A < B ≤ 1, w(z) ∈ H. Let S*(A, B) denote the class of functions f(z) of the form such that zf′(z)/f(z) ∈ P(A, B). If f(z) ∈ S*(A, B) and g(z) ∈ S*(C, D) then, in this paper the radius of starlikeness of order β (β ∈ [0, 1]) of the following integral operatoris determined. Conversely, a sharp estimate is obtained for the radius of starlikeness of the class of functionswhere g(z) and F(z) belong to the class S*(A, B).

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 A Generalized Class of Functions Defined by the q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2361
Author(s):  
Loriana Andrei ◽  
Vasile-Aurel Caus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
The Relationship ◽  
Class Of Functions

The goal of the present investigation is to introduce a new class of analytic functions (Kt,q), defined in the open unit disk, by means of the q-difference operator, which may have symmetric or assymetric properties, and to establish the relationship between the new defined class and appropriate subordination. We derived relationships of this class and obtained sufficient conditions for an analytic function to be Kt,q. Finally, in the concluding section, we have taken the decision to restate the clearly-proved fact that any attempt to create the rather simple (p,q)-variations of the results, which we have provided in this paper, will be a rather inconsequential and trivial work, simply because the added parameter p is obviously redundant.

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