scholarly journals Some Results of Differential Subordination and Differential Superordination Theorems for Univalent Functions Defined by Ruscheweyh Derivative Operator

2019 ◽  
Vol 3 (2) ◽  
pp. 432
Author(s):  
Aqeel AL-khafaji
Keyword(s):  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Creative Commons ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Differential Superordination ◽  
Open Access Article

The purpose of the present paper is to derive several subordination, superordination results, and sandwich results for the function of the form $f\left(z\right)=z+\sum^{\infty }_{n=2}{a_nz^n}$ which is univalent in the open unit disc $\ U=\left\{z\in \mathbb{C}:\left|z\right|.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

scholarly journals Some Properties for Strong Differential Subordination of Analytic Functions Involving Ruscheweyh Derivative Operator

2020 ◽  
pp. 63-70
Author(s):  
Asraa Abdul Jaleel Husien
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Derivative Operator ◽  
Closed Unit Disk ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Strong Differential Subordination ◽  
Differential Subordinations

In this paper, we introduce and study some properties for strong differential subordinations of analytic functions associated with Ruscheweyh derivative operator defined in the open unit disk and closed unit disk of the complex plane.

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

2019 ◽  
Vol 12 (03) ◽  
pp. 1950035
Author(s):  
Ritu Agarwal ◽  
G. S. Paliwal ◽  
Parany Goswami
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Sandwich Theorem ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Principle Of Subordination ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

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.

scholarly journals Coefficient estimates for families of bi-univalent functions defined by Ruscheweyh derivative operator

2021 ◽  
Vol 25 (1) ◽  
pp. 71-80
Author(s):  
Serap Bulut ◽  
Wanas Kareem
Keyword(s):  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Special Cases

The main purpose of this manuscript is to find upper bounds for the second and third Taylor-Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Ruscheweyh derivative operator. Further, we point out certain special cases for our results.

scholarly journals Hankel determinant for certain class of analytic function defined by generalized derivative operator

2012 ◽  
Vol 43 (3) ◽  
pp. 445-453
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Upper Bound ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Generalised Derivatives

The authors in \cite{mam1} have recently introduced a new generalised derivatives operator $ \mu_{\lambda _1 ,\lambda _2 }^{n,m},$ which generalised many well-known operators studied earlier by many different authors. By making use of the generalised derivative operator $\mu_{\lambda_1 ,\lambda _2 }^{n,m}$, the authors derive the class of function denoted by $ \mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$, which contain normalised analytic univalent functions $f$ defined on the open unit disc $U=\left\{{z\,\in\mathbb{C}:\,\left| z \right|\,<\,1} \right\}$ and satisfy \begin{equation*}{\mathop{\rm Re}\nolimits} \left( {\mu _{\lambda _1 ,\lambda _2 }^{n,m} f(z)} \right)^\prime > 0,\,\,\,\,\,\,\,\,\,(z \in U).\end{equation*}This paper focuses on attaining sharp upper bound for the functional $\left| {a_2 a_4 - a_3^2 } \right|$ for functions $f(z)=z+ \sum\limits_{k = 2}^\infty {a_k \,z^k }$ belonging to the class $\mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$.

scholarly journals A certain q-Ruscheweyh type derivative operator and its applications involving multivalent functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bilal Khan ◽  
H. M. Srivastava ◽  
Sama Arjika ◽  
Shahid Khan ◽  
Nazar Khan ◽  
...  
Keyword(s):  
Difference Operator ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative

AbstractIn the present paper, by using the concept of convolution and q-calculus, we define a certain q-derivative (or q-difference) operator for analytic and multivalent (or p-valent) functions. This presumably new q-derivative operator is an extension of the known q-analogue of the Ruscheweyh derivative operator. We also give some interesting applications of this q-derivative operator for multivalent functions by using the method of differential subordination. Relevant connections with a number of earlier works on this subject are also pointed out.

scholarly journals On a certain subclass of analytic functions defined by a generalized S˘al˘agean operator and Ruscheweyh derivative

2012 ◽  
Vol 28 (2) ◽  
pp. 183-190
Author(s):  
ALINA ALB LUPAS ◽  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disc ◽  
Ruscheweyh Derivative ◽  
Differential Subordinations

In the present paper we define a new operator using the generalized Sal˘ agean and Ruscheweyh operators. Denote by ˘ RDm λ,α the operator given by RDm λ,α : An → An, RDm λ,αf(z) = (1 − α)Rmf(z) + αDm λ f(z), z ∈ U, where Rmf(z) denote the Ruscheweyh derivative, Dm λ f(z) is the generalized Sal˘ agean operator and ˘ An = {f ∈ H(U) : f(z) = z +an+1z n+1 +. . . , z ∈ U} is the class of normalized analytic functions. A certain subclass, denoted by RDm (δ, λ, α) , of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class RDm (δ, λ, α) . Also, several differential subordinations are established regarding the operator RDm λ,α.

scholarly journals On Sandwich Theorems for Certain Univalent Functions Defined by a New operator

2019 ◽  
Vol 11 (2) ◽  
pp. 72-80 ◽  
Author(s):  
Waggas Galib Atshan ◽  
Elaf Ibrahim Badawi
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disc ◽  
Differential Subordination And Superordination

In this paper, we study some differential subordination and superordination results for certain univalent functions in the open unit disc U by using a new operator . Also, we derive some sandwich theorems.

scholarly journals On Differential Subordination and Superordination for Univalent Function Involving New Operator

2022 ◽  
pp. 22-31
Author(s):  
Mustafa I. Hameed ◽  
Buthyna Najad Shihab
Keyword(s):  
Integral Operator ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Linear Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
Third Order ◽  
Differential Subordination And Superordination ◽  
Shed Light

The goal of this paper is to investigate some of the features of differential subordination of analytic univalent functions in an open unit disc. In addition, it has shed light on geometric features such as coefficient inequality, Hadamard product qualities, and the Komatu integral operator. Some intriguing results for third-order differential subordination and superordination of analytic univalent functions have been installed. Then, using the convolution of two linear operators, certain results of third order differential subordination involving linear operators were reported. As a result, we use features of the Komatu integral operator to analyze and study third-order subordinations and superordinations in relation to the convolution. Finally, several results for third order differential subordination in the open unit disk using generalized hypergeometric function have been addressed using the convolution operator.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

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