scholarly journals Applications of a New q -Difference Operator in Janowski-Type Meromorphic Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Bakhtiar Ahmad ◽  
Muhammad Ghaffar Khan ◽  
Mohamed Kamal Aouf ◽  
Wali Khan Mashwani ◽  
Zabidin Salleh ◽  
...  
Keyword(s):  
Differential Operator ◽  
Convex Functions ◽  
Difference Operator ◽  
Algebraic Property ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Radius Of Convexity

The main aim of the present article is the introduction of a new differential operator in q -analogue for meromorphic multivalent functions which are analytic in punctured open unit disc. A subclass of meromorphic multivalent convex functions is defined using this new differential operator in q -analogue. Furthermore, we discuss a number of useful geometric properties for the functions belonging to this class such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity. Also, algebraic property of closure is discussed of functions belonging to this class. Integral representation problem is also proved for these functions.

scholarly journals Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1840
Author(s):  
Lei Shi ◽  
Bakhtiar Ahmad ◽  
Nazar Khan ◽  
Muhammad Ghaffar Khan ◽  
Serkan Araci ◽  
...  
Keyword(s):  
Differential Operator ◽  
Convex Functions ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
New Class ◽  
Radius Of Convexity

By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

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 Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

scholarly journals Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

Further results for two certain subclasses of close-to-convex functions

2020 ◽  
pp. 2150045
Author(s):  
H. Mahzoon ◽  
R. Kargar
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Family ◽  
Radius Of Univalence

Let [Formula: see text] be the family of analytic and normalized functions [Formula: see text] in the open unit disc [Formula: see text]. In this paper, we consider the following classes: [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text]. We show that if [Formula: see text], then [Formula: see text] and [Formula: see text] are greater than [Formula: see text], and if [Formula: see text], then [Formula: see text]. Also, some another interesting properties of the class [Formula: see text] are investigated. Finally, the radius of univalence of 2nd section sum of [Formula: see text] is obtained.

scholarly journals Certain Subclasses of β-Uniformly q-Starlike and β-Uniformly q-Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Eman S. A. AbuJarad ◽  
Mohammed H. A. AbuJarad ◽  
Thabet Abdeljawad ◽  
Fahd Jarad
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Coefficient Bounds

In this paper, the authors introduced certain subclasses β-uniformly q-starlike and β-uniformly q-convex functions of order α involving the q-derivative operator defined in the open unit disc. Coefficient bounds were also investigated.

scholarly journals Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Saibah Siregar ◽  
Maslina Darus
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Subordination Result ◽  
Jack’S Lemma ◽  
Jack's Lemma

For , , we consider the of normalized analytic convex functions defined in the open unit disc . In this paper, we investigate the class , that is, , with is Koebe type, that is, . The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class of -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

scholarly journals Some Geometric Properties for a Certain Class of Meromorphic Univalent Functions by Differential Operator

2021 ◽  
pp. 2667-2675
Author(s):  
Mohammed Hadi Lafta
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Growth Theorem ◽  
Closure Theorem ◽  
Major Target ◽  
Meromorphic Univalent Functions

The major target of this paper is to study a confirmed class of meromorphic univalent functions . We procure several results, such as those related to coefficient estimates, distortion and growth theorem, radii of starlikeness, and convexity for this class, n additionto hadamard product, convex combination, closure theorem, integral operators, and  neighborhoods.

scholarly journals Best Dominants and Subordinants for Certain Sandwich-Type Theorems

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 62
Author(s):  
Adriana Cătaş ◽  
Emilia Borşa ◽  
Loredana Iambor
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Symmetric Domain ◽  
Open Unit ◽  
Open Unit Disc ◽  
Sandwich Type

In this paper, we aim to present a survey on subordination and superordination theorems related to the class of analytic functions defined in a symmetric domain, which is the open unit disc. The results were deduced by making use of a new differential operator. We present two properties of this operator from which we constructed the final results. Moreover, based on the obtained outcomes, we give two sandwich-type theorems. Some interesting further consequences are also taken into consideration.

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