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 Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

scholarly journals A New Class of Analytic Functions Defined by Using Salagean Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Integral Means ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

scholarly journals Certain classes of analytic functions defined by fractional q-calculus operator

2018 ◽  
Vol 10 (1) ◽  
pp. 178-188 ◽  
Author(s):  
N. Ravikumar
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Open Disc ◽  
Inclusion Relations

Abstract In this paper, the concept of fractional q-calculus and generalized Al-Oboudi differential operator defining certain classes of analytic functions in the open disc are used. The results investigated for these classes of functions include the coefficient estimates, inclusion relations, extreme points and some more properties.

Some properties of a subclass of uniformly convex functions with negative coefficients

2008 ◽  
Vol 41 (2) ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions

AbstractThe aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass

scholarly journals Solvability of a New q-Differential Equation Related to q-Differential Inequality of a Special Type of Analytic Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 228
Author(s):  
Ibtisam Aldawish ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Analytic Functions ◽  
Differential Inequality ◽  
Laguerre Polynomial ◽  
Analytic Solutions ◽  
Confluent Hypergeometric Function ◽  
Differential Inequalities ◽  
Quantum Calculus

The current study acts on the notion of quantum calculus together with a symmetric differential operator joining a special class of meromorphic multivalent functions in the puncher unit disk. We formulate a quantum symmetric differential operator and employ it to investigate the geometric properties of a class of meromorphic multivalent functions. We illustrate a set of differential inequalities based on the theory of subordination and superordination. In this real case study, we found the analytic solutions of q-differential equations. We indicate that the solutions are given in terms of confluent hypergeometric function of the second type and Laguerre polynomial.

scholarly journals A Certain Subclass of Multivalent Analytic Functions with Negative Coefficients for Operator on Hilbert Space

2019 ◽  
pp. 355-364
Author(s):  
Asraa Abdul Jaleel Husien
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

In the present work, we introduce and study a certain subclass for multivalent analytic functions with negative coefficients defined on complex Hilbert space. We establish a number of geometric properties, like, coefficient estimates, convex set, extreme points and radii of starlikeness and convexity.

scholarly journals New Family of Multivalent Analytic Functions Defined on Complex Hilbert Space

2020 ◽  
pp. 155-165 ◽  
Author(s):  
Abbas Kareem Wanas ◽  
S. R. Swamy
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
New Family

In this article, we define a certain new class of multivalent analytic functions with negative coefficients on complex Hilbert space. We derive a number of important geometric properties, such as, coefficient estimates, radii of starlikeness and convexity, extreme points and convex set.

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 Applications of Borel Distribution Series on Analytic Functions

2020 ◽  
pp. 71-82
Author(s):  
Abbas Kareem Wanas ◽  
Jubran Abdulameer Khuttar
Keyword(s):  
Power Series ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sigma Delta ◽  
The Family ◽  
Necessary And Sufficient

The purpose of the present paper is to determine the necessary and sufficient conditions for the power series B_{\mu} whose coefficients are probabilities of the Borel distribution to be in the family H(\lambda, \sigma, \delta, \mu) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral representation, radii of starlikeness and convexity. Also we discuss the extreme points and neighborhood property for functions belongs to this family.

scholarly journals Some subclasses of analytic functions of complex order defined by new differential operator

2012 ◽  
Vol 43 (2) ◽  
pp. 223-242
Author(s):  
Maslina Darus ◽  
Imran Faisal
Keyword(s):  
Differential Operator ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Fractional Differential Operator ◽  
Alpha Omega ◽  
Fractional Differential ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

Let \hskip 2pt $\mathcal{A}(n)$ \hskip 2pt denote \hskip 2pt the \hskip 2pt class \hskip 2pt of \hskip 2pt analytic \hskip 2pt functions \hskip 2pt $f$ \hskip 2pt in \hskip 2pt the \hskip 2pt open \hskip 2pt unit \hskip 2pt disk \hskip 2pt $U=\{z:|z|<1\}$ \hskip 2pt normalized \hskip 2pt by \hskip 2pt $f(0)=f'(0)-1=0.$ \hskip 2pt In \hskip 2pt this \hskip 2pt paper, \hskip 2pt we \hskip 2pt introduce \hskip 2pt and \hskip 2pt study \hskip 2pt the \hskip 2pt classes \hskip 2pt $S_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho)$ \hskip 2pt and \hskip 2pt $R_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho)$ \hskip 2pt of \hskip 2pt functions \hskip 2pt $f\in\mathcal{A}(n)$ with $(\mu)z(D^{\mho+2}_{\lambda}(\alpha, \omega)f(z))'+(1-\mu)z(D^{\mho+1}_{\lambda}(\alpha, \omega)f(z))'\neq0$ and satisfy some conditions available in literature, where $f\in\mathcal{A}(n), \alpha, \omega, \lambda, \mu \geq0, \mho\in \mathbb{N}\cup\{0\},\,\,z\in U,$ and $D^{m}_{\lambda}(\alpha, \omega)f(z): \mathcal{A}\rightarrow \mathcal{A},$ is the linear fractional differential operator, newly defined as follows $$D^{m}_{\lambda}(\alpha, \omega)f(z) = z+ \sum\limits_{k=2}^{\infty}a_{k}(1+(k-1)\lambda \omega^{\alpha})^{m}z^{k}\cdot$$ Several properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion for the functions included in the classes $S_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho, \omega)$ and $R_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho, \omega)$ are given.

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