scholarly journals A novel subclass of analytic functions specified by a family of fractional derivatives in the complex domain

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2837-2849
Author(s):  
Zainab Esa ◽  
H.M. Srivastava ◽  
Adem Kılıçman ◽  
Rabha Ibrahim
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Univalent Functions ◽  
Complex Domain ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Fractional Derivative Operators ◽  
Coefficient Inequalities ◽  
Distortion Theorems ◽  
Analytic And Univalent Functions

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass P?,?(k,?,?) of analytic and univalent functions in the open unit disk U. In particular, for functions in the class P?,?(k,?,?), we derive sufficient coefficient inequalities and coefficient estimates, distortion theorems involving the above-mentioned fractional derivative operators, and the radii of starlikeness and convexity. In addition, some applications of functions in the class P?,?(k,?,?) are also pointed out.

scholarly journals Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 172 ◽  
Author(s):  
Hari M. Srivastava ◽  
Ahmad Motamednezhad ◽  
Ebrahim Analouei Adegani
Keyword(s):  
Fractional Derivative ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Faber Polynomial

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 306 ◽  
Author(s):  
Suhila Elhaddad ◽  
Maslina Darus
Keyword(s):  
Unit Disk ◽  
Systematic Study ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Coefficient Inequalities

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

scholarly journals On Subclass of Analytic Univalent Functions Associated with Negative Coefficients

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Closure Theorems ◽  
Coefficient Inequalities ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

M. H. Al-Abbadi and M. Darus (2009) recently introduced a new generalized derivative operatorμλ1,λ2n,m, which generalized many well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit diskU={z∈ℂ:|z|<1}which is defined by new generalized derivative operator. Some results on coefficient inequalities, growth and distortion theorems, closure theorems, and extreme points of analytic functions belonging to the subclass are obtained.

scholarly journals ON CERTAIN SUBCLASS OF UNIVALENT FUNCTIONS IN THE UNIT DISC I

1995 ◽  
Vol 26 (4) ◽  
pp. 299-312
Author(s):  
M. K. AOUF ◽  
A. SHAMANDY ◽  
M. F. YASSEN
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Closure Theorems ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Analytic And Univalent Functions

The object of the present paper is to derive several interesting proper- ties of the class $P_n(\alpha, \beta, \gamma)$ consisting of analytic and univalent functions with neg- ative coefficients. Coefficient estimates, distortion theorems and closure theorems of functions in the class $P_n(\alpha, \beta, \gamma)$ are determined. Also radii of close-to-convexity, starlikeness and convexity and integral operators are determined.

Some Properties of the Class of Univalent Functions Involving a New Generalized Differential Operator

2016 ◽  
Vol 13 (10) ◽  
pp. 6797-6799
Author(s):  
A. A Amourah ◽  
T Al-Hawary ◽  
M Darus
Keyword(s):  
Differential Operator ◽  
Integral Operator ◽  
Univalent Functions ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Generalized Differential ◽  
Growth And Distortion Theorems

The main purpose of this paper is to introduce new generalized differential operator Aμm, λ(α,β)f(z) defined in the open unit disc U = {z ∈ : |z| < 1}. We then, using this operator to introduce novel subclass Ωm*(δ,λ,α,β,b) by using the operator Aμm, λ(α,β)f(z). Then, we discuss coefficient estimates growth and distortion theorems, closure theorems and integral operator.

scholarly journals A Certain Subclass of Analytic and Univalent Functions Defined by Hadamard Product

2019 ◽  
pp. 87-99
Author(s):  
Dhirgam Allawy Hussein ◽  
Sahar Jaafar Mahmood
Keyword(s):  
Hadamard Product ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Analytic And Univalent Functions

In this paper, we present a new subclass AD(l, g, a, b) of analytic univalent functions in the open unit disk U. We establish some interesting properties like, coefficient estimates, closure theorems, extreme points, growth and distortion theorem and radius of starlikeness and convexity.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
S. P. Goyal ◽  
Rakesh Kumar
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

AbstractIn the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f

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