scholarly journals Differential Subordination Defined by New Generalised Derivative Operator for Analytic Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator

A new generalised derivative operatorμλ1,λ2n,mis introduced. This operator generalised many well-known operators studied earlier by many authors. Using the technique of differential subordination, we will study some of the properties of differential subordination. In addition we investigate several interesting properties of the new generalised derivative operator.

scholarly journals Differential Subordination with Generalized Derivative Operator of Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Entisar El-Yagubi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Generalized Derivative

Motivated by generalized derivative operator defined by the authors (El-Yagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator Dλ1,λ2,δm,b are given.

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 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.

scholarly journals Subclasses of Multivalent Analytic Functions Associated with a q-Difference Operator

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2184
Author(s):  
Ekram Elsayed Ali ◽  
Teodor Bulboacă
Keyword(s):  
Analytic Functions ◽  
Difference Operator ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Inclusion Properties ◽  
Subordination Theory

In this article we introduced and studied some inclusion properties for new subclasses of multivalent analytic functions defined by using the q-derivative operator. With the aid of the Jackson q-derivative we defined two new operators that generalize many other previously studied operators, and help us to define two new subclasses of functions with several interesting properties studied in this paper. The methods used for the proof of our results are special tools of the differential subordination theory of one-variable functions.

Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 160
Author(s):  
Likai Liu ◽  
Jin-Lin Liu
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Lemniscate Of Bernoulli

Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1<1. Several previous results are extended.

Differential sandwich theorems of p-valent functions defined by a certain linear operator

2016 ◽  
Vol 53 (2) ◽  
pp. 131-137
Author(s):  
Ping He ◽  
Defei Zhang
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Subordination And Superordination

In this paper we introduce differential subordination and superordination properties for certain subclasses of analytic functions involving certain linear operator, and obtain sandwich-type results for the functions belonging to these classes.

scholarly journals Second Hankel determinant for a class of analytic functions defined by q-derivative operator

2019 ◽  
Vol 27 (2) ◽  
pp. 167-177
Author(s):  
Dorina Răducanu
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
Second Hankel Determinant

AbstractIn this paper, we obtain the estimates for the second Hankel determinant for a class of analytic functions defined by q-derivative operator and subordinate to an analytic function.

scholarly journals On Certain Subclasses of Analytic Functions Defined by Differential Subordination

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Hesam Mahzoon
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Radius Of Starlikeness ◽  
Covering Theorems ◽  
Coefficient Inequalities

We introduce and study certain subclasses of analytic functions which are defined by differential subordination. Coefficient inequalities, some properties of neighborhoods, distortion and covering theorems, radius of starlikeness, and convexity for these subclasses are given.

Operational Identities for Circular and Hyperbolic Functions and Their Generalizations

2003 ◽  
Vol 10 (1) ◽  
pp. 45-56 ◽  
Author(s):  
C. Cassisa ◽  
P. E. Ricci ◽  
I. Tavkhelidze
Keyword(s):  
Analytic Functions ◽  
Operational Calculus ◽  
Hyperbolic Functions ◽  
Derivative Operator ◽  
Circular Functions

Abstract Starting from the exponential, some classes of analytic functions of the derivative operator are studied, including pseudo-hyperbolic and pseudo-circular functions. Some formulas related to operational calculus are deduced, and the important role played in such a context by Hermite–Kampé de Fériet polynomials is underlined.

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