Differential Subordination And Convex Univalent Functions

2019 ◽  
Vol 65 (9) ◽  
pp. 30-36
Author(s):  
Aarthi S
Keyword(s):  
Univalent Functions ◽  
Differential Subordination ◽  
Convex Univalent Functions

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 Region of Variability for Exponentially Convex Univalent Functions

2010 ◽  
Vol 5 (3) ◽  
pp. 955-966 ◽  
Author(s):  
Ponnusamy Saminathan ◽  
Vasudevarao Allu ◽  
M. Vuorinen
Keyword(s):  
Univalent Functions ◽  
Convex Univalent Functions

scholarly journals Applications of Certain Operators to the Classes of Analytic Functions Related to the Generalized Janowski Functions

2020 ◽  
pp. 211-225
Author(s):  
Khalida Inayat Noor ◽  
Shujaat Ali Shah
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Linear Operators ◽  
Janowski Functions ◽  
Radius Problems ◽  
Convex Univalent Functions

We introduce certain subclasses of analytic functions related to the class of analytic, convex univalent functions. We discuss some results including inclusion relationships and invariance of the classes under convex convolution in terms of certain linear operators. Applications of these results associated with the generalized Janowski functions and conic domains are considered. Also, several radius problems are investigated.

scholarly journals On Sandwich Theorems Results for Certain Univalent Functions Defined by Generalized Operators

2021 ◽  
pp. 2376-2383
Author(s):  
Waggas Galib Atshan ◽  
Aqeel Ahmed Redha Ali
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordination And Superordination

In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.

On a Differential Subordination of a Certain Subclass of Univalent Functions

2018 ◽  
Vol 5 (3) ◽  
pp. 11-16
Author(s):  
Aqeel AL-khafaji ◽  
◽  
Waggas Atshan ◽  
Salwa Abed ◽  
◽  
...  
Keyword(s):  
Univalent Functions ◽  
Differential Subordination

UNIVALENCE CONDITIONS FOR A NEW INTEGRAL OPERATOR

2015 ◽  
Vol 1 (2) ◽  
pp. 35-37
Author(s):  
Sh. Najafzadeh ◽  
A. Ebadian ◽  
H. Rahmatan
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Norm Estimates ◽  
Schwarzian Derivatives ◽  
Convex Univalent Functions

In the present paper, we will obtain norm estimates of the pre-Schwarzian derivatives for $F_{\lambda,\mu}(z)$, such that \[ F_{\lambda,\mu}(z) = \int_0^z \prod_{i=1}^{n} (f'_i(t))^{\lambda_i}\left( \frac{f_i(t)}{t} \right)^{\mu_i}dt \quad (z\in D),\] where $\lambda_i,\mu_i\in \mathbb{R}$, $\lambda_i=(\lambda_1,\lambda_2,\ldots,\lambda_n$, $\mu_i=(\mu_1,\mu_2,\ldots,\mu_n$ and $f_i$ belongs to the class of convex univalent functions $\mathcal{C}\subset \mathcal{S}$.

"Some Results of Differential Subordination and Superordination for Univalent Functions

2021 ◽  
Vol 8 (1) ◽  
pp. 91-97
Author(s):  
Ihsan A. Abbas
Keyword(s):  
Univalent Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Type Result ◽  
Best Dominant ◽  
Subordination Chain ◽  
Sandwich Type ◽  
Differential Subordination And Superordination

"Let 1 and 2 belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions to satisfy the double subordination chain 1() ≺() ≺ 2() , then we obtain 1() is the best subordinant, 2() is the best dominant. Also we derive some sandwich –type result.

scholarly journals Quasi-convex univalent functions

1980 ◽  
Vol 3 (2) ◽  
pp. 255-266 ◽  
Author(s):  
K. Inayat Noor ◽  
D. K. Thomas
Keyword(s):  
Univalent Functions ◽  
New Class ◽  
Convex Univalent Functions

In this paper, a new class of normalized univalent functions is introduced. The properties of this class and its relationship with some other subclasses of univalent functions are studied. The functions in this class are close-to-convex.

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