"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 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.

scholarly journals Strong Differential Subordinations Obtained with New Integral Operator Defined by Polylogarithm Function

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
K. AL-Shaqsi
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Polylogarithm Function ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Strong Differential Subordination ◽  
Differential Subordinations ◽  
Admissible Functions

By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.

scholarly journals Differential subordination and superordination results for certain subclasses of analytic functions by the technique of admissible functions

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2009-2026
Author(s):  
R. Jayasankar ◽  
Maslina Darus ◽  
S. Sivasubramanian
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

By investigating appropriate classes of admissible functions, various Differential subordination and superordination results for analytic functions in the open unit disk are obtained using Cho-Kwon-Srivastava operator. As a consequence of these results, Sandwich-type results are also obtained.

scholarly journals The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1083 ◽  
Author(s):  
Nak Eun Cho ◽  
Mohamed Kamal Aouf ◽  
Rekha Srivastava
Keyword(s):  
Fractional Derivative ◽  
Integral Operators ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Family ◽  
Sandwich Type ◽  
Fractional Differintegral ◽  
Generalized Fractional Derivative ◽  
Fractional Differintegral Operator

A useful family of fractional derivative and integral operators plays a crucial role on the study of mathematics and applied science. In this paper, we introduce an operator defined on the family of analytic functions in the open unit disk by using the generalized fractional derivative and integral operator with convolution. For this operator, we study the subordination-preserving properties and their dual problems. Differential sandwich-type results for this operator are also investigated.

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 On Fully-Convex Harmonic Functions and their Extension

2018 ◽  
Vol 38 (2) ◽  
pp. 51-60
Author(s):  
Shahpour Nosrati ◽  
Ahmad Zireh
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Circular Arc ◽  
Coefficient Condition ◽  
Necessary And Sufficient ◽  
Convex Univalent Functions

‎Uniformly convex univalent functions that introduced by Goodman‎, ‎maps every circular arc contained in the open unit disk with center in it into a convex curve‎. ‎On the other hand‎, ‎a fully-convex harmonic function‎, ‎maps each subdisk $|z|=r<1$ onto a convex curve‎. ‎Here we synthesis these two ideas and introduce a family of univalent harmonic functions which are fully-convex and uniformly convex also‎. ‎In the following we will mention some examples of this subclass and obtain a necessary and sufficient conditions and finally a coefficient condition will attain with convolution‎.

scholarly journals On applications of differential subordination and superordination

2008 ◽  
Vol 39 (2) ◽  
pp. 155-164
Author(s):  
N. Marikkannan ◽  
C. Ganesamoorthy
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Ruscheweyh Derivative ◽  
Differential Subordination And Superordination

In the present investigation we obtain the sufficient conditions for normalized analytic functions $f$ to satisfy$$ q_1 \prec \frac{f^2}{z^2f'} \prec q_2, $$where $ q_1 $ and $ q_2 $ are univalent functions with $ q_1(0)= q_2(0)=1 $. Also we obtain the sandwich results involving Carlson-Shaffer linear operator, $ S\u{a}l\u{a} $gean derivative and Ruscheweyh derivative.

scholarly journals On q-ANALOGUE of Differential Subordination Associated with Lemniscate of Bernoulli

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mohsan Raza ◽  
Hira Naz ◽  
Sarfraz Nawaz Malik ◽  
Sahidul Islam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Lemniscate Of Bernoulli

This article comprises the study of differential subordination with analogue of q -derivative. It includes the sufficient condition on γ for 1 + γ ∂ z q h z / h n z to be subordinated by 1 + A z / 1 + B z , − 1 ≤ B < A ≤ 1 , and implies that h z ≺ 1 + z , where h z is the analytic function in the open unit disk. Moreover, certain sufficient conditions for q -starlikeness of analytic functions related with lemniscate of Bernoulli are determined.

scholarly journals New and Extended Results On Fourth-Order Differential Subordination for Univalent Analytic Functions

2020 ◽  
Vol 25 (2) ◽  
pp. 1-13 ◽  
Author(s):  
Waggas Galib Atshan ◽  
Ali Hussein Battor ◽  
Abeer Farhan Abaas ◽  
Georgia Irina Oros
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Fourth Order ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordination And Superordination

In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with linear operator for univalent analytic functions in open unit disk. Here, we extended some lemmas. Also  some interesting new results are obtained.

scholarly journals Certain subclasses of Spiral-like univalent functions related with Pascal distribution series

2021 ◽  
Vol 7 (2) ◽  
pp. 312-323
Author(s):  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Inclusion Relations ◽  
Pascal Distribution

Abstract The purpose of the present paper is to find the sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations for such subclasses in the open unit disk 𝔻. Further, we consider the properties of integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

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