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 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 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 COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS OF COMPLEX ORDER

2011 ◽  
Vol 15 (5) ◽  
pp. 2377-2386 ◽  
Author(s):  
Qing-Hua Xu ◽  
Ying-Chun Gui ◽  
H. M. Srivastava
Keyword(s):  
Analytic Functions ◽  
Coefficient Estimates ◽  
Complex Order

scholarly journals A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 458 ◽  
Author(s):  
Muhammad Naeem ◽  
Saqib Hussain ◽  
Tahir Mahmood ◽  
Shahid Khan ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Coefficient Estimates ◽  
Quantum Calculus

In our present investigation, we use the technique of convolution and quantum calculus to study the Salagean q-differential operator. By using this operator and the concept of the Janowski function, we define certain new classes of analytic functions. Some properties of these classes are discussed, and numerous sharp results such as coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, and integral mean inequalities of functions belonging to these classes are obtained and studied.

scholarly journals Coefficient Estimates and Other Properties for a Class of Spirallike Functions Associated with a Differential Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Halit Orhan ◽  
Dorina Răducanu ◽  
Murat Çağlar ◽  
Mustafa Bayram
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
New Class ◽  
Spirallike Functions

For , , , , and , a new class of analytic functions defined by means of the differential operator is introduced. Our main object is to provide sharp upper bounds for Fekete-Szegö problem in . We also find sufficient conditions for a function to be in this class. Some interesting consequences of our results are pointed out.

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.

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