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Search Results (7)

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Keywords = q-Ruscheweyh derivative operator

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22 pages, 378 KiB  
Article
A Novel Family of Starlike Functions Involving Quantum Calculus and a Special Function
by Baseer Gul, Daniele Ritelli, Reem K. Alhefthi and Muhammad Arif
Fractal Fract. 2025, 9(3), 179; https://doi.org/10.3390/fractalfract9030179 - 14 Mar 2025
Cited by 2 | Viewed by 587
Abstract
The intent of quantum calculus, briefly q-calculus, is to find q-analogues of mathematical entities so that the original object is achieved when a certain limit is taken. In the case of q-analogue of the ordinary derivative, the limit is [...] Read more.
The intent of quantum calculus, briefly q-calculus, is to find q-analogues of mathematical entities so that the original object is achieved when a certain limit is taken. In the case of q-analogue of the ordinary derivative, the limit is q1. Also, the study of integral as well as differential operators has remained a significant field of inquiry from the early developments of function theory. In the present article, a subclass Sscμ,q of functions being analytic in D=zC:z<1 is introduced. The definition of Sscμ,q involves the concepts of subordination, that of q-derivative and q-Ruscheweyh operators. Since coefficient estimates and coefficient functionals provide insights into different geometric properties of analytic functions, for this newly defined subclass, we investigate coefficient estimates up to a4, in which both bounds for |a2| and |a3| are sharp, while that of |a4| is sharp in one case. We also discuss the sharp Fekete–Szegö functional for the said class. In addition, Toeplitz determinant bounds up to T32 (sharp in some cases) and sufficient condition are obtained. Several consequences derived from our above-mentioned findings are also part of the discussion. Full article
20 pages, 316 KiB  
Article
Subordinations Results on a q-Derivative Differential Operator
by Loriana Andrei and Vasile-Aurel Caus
Mathematics 2024, 12(2), 208; https://doi.org/10.3390/math12020208 - 8 Jan 2024
Cited by 6 | Viewed by 2192
Abstract
In this research paper, we utilize the q-derivative concept to formulate specific differential and integral operators denoted as Rqn,m,λ, Fqn,m,λ and Gqn,m,λ. [...] Read more.
In this research paper, we utilize the q-derivative concept to formulate specific differential and integral operators denoted as Rqn,m,λ, Fqn,m,λ and Gqn,m,λ. These operators are introduced with the aim of generalizing the class of Ruscheweyh operators within the set of univalent functions. We extract certain properties and characteristics of the set of differential subordinations employing specific techniques. By utilizing the newly defined operators, this paper goes on to establish subclasses of analytic functions defined on an open unit disc. Additionally, we delve into the convexity properties of the two recently introduced q-integral operators, Fqn,m,λ and Gqn,m,λ. Special cases of the primary findings are also discussed. Full article
15 pages, 303 KiB  
Article
Bounds for Toeplitz Determinants and Related Inequalities for a New Subclass of Analytic Functions
by Huo Tang, Ihtesham Gul, Saqib Hussain and Saima Noor
Mathematics 2023, 11(18), 3966; https://doi.org/10.3390/math11183966 - 18 Sep 2023
Cited by 5 | Viewed by 1296
Abstract
In this article, we use the q-derivative operator and the principle of subordination to define a new subclass of analytic functions related to the q-Ruscheweyh operator. Sufficient conditions, sharp bounds for the initial coefficients, a Fekete–Szegö functional and a Toeplitz determinant [...] Read more.
In this article, we use the q-derivative operator and the principle of subordination to define a new subclass of analytic functions related to the q-Ruscheweyh operator. Sufficient conditions, sharp bounds for the initial coefficients, a Fekete–Szegö functional and a Toeplitz determinant are investigated for this new class of functions. Additionally, we also present several established consequences derived from our primary findings. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory)
11 pages, 282 KiB  
Article
Some Subordination Results Defined by Using the Symmetric q-Differential Operator for Multivalent Functions
by Saima Noor, Sa’ud Al-Sa’di and Saqib Hussain
Axioms 2023, 12(3), 313; https://doi.org/10.3390/axioms12030313 - 22 Mar 2023
Cited by 3 | Viewed by 1514
Abstract
In this article, we use the concept of symmetric q-calculus and convolution in order to define a symmetric q-differential operator for multivalent functions. This operator is an extension of the classical Ruscheweyh differential operator. By using the technique of differential subordination, [...] Read more.
In this article, we use the concept of symmetric q-calculus and convolution in order to define a symmetric q-differential operator for multivalent functions. This operator is an extension of the classical Ruscheweyh differential operator. By using the technique of differential subordination, we derive several interesting applications of the newly defined operator for multivalent functions. Full article
12 pages, 308 KiB  
Article
Certain Inclusion Properties for the Class of q-Analogue of Fuzzy α-Convex Functions
by Abdel Fatah Azzam, Shujaat Ali Shah, Alhanouf Alburaikan and Sheza M. El-Deeb
Symmetry 2023, 15(2), 509; https://doi.org/10.3390/sym15020509 - 14 Feb 2023
Cited by 6 | Viewed by 1641
Abstract
Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect [...] Read more.
Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis. We introduce the family of linear q-operators and define various classes associated with these operators. The inclusion results and various integral properties are the main investigations of this article. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
18 pages, 309 KiB  
Article
On q-Starlike Functions Defined by q-Ruscheweyh Differential Operator in Symmetric Conic Domain
by Saira Zainab, Mohsan Raza, Qin Xin, Mehwish Jabeen, Sarfraz Nawaz Malik and Sadia Riaz
Symmetry 2021, 13(10), 1947; https://doi.org/10.3390/sym13101947 - 16 Oct 2021
Cited by 16 | Viewed by 2138
Abstract
Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to [...] Read more.
Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to first define and then study a new class of holomorphic functions using the q-Ruscheweyh differential operator. A new class kSTqτC,D of k-Janowski starlike functions associated with the symmetric conic domain, which are defined by the generalized Ruscheweyh derivative operator in the open unit disk, is introduced. The necessary and sufficient condition for a function to be in the class kSTqτC,D is established. In addition, the coefficient bound, partial sums and radii of starlikeness for the functions from the class of k-Janowski starlike functions related with symmetric conic domain are included. Full article
(This article belongs to the Special Issue Complex Analysis, in Particular Analytic and Univalent Functions)
13 pages, 258 KiB  
Article
Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions
by Shahid Mahmood, Hari M. Srivastava, Nazar Khan, Qazi Zahoor Ahmad, Bilal Khan and Irfan Ali
Symmetry 2019, 11(3), 347; https://doi.org/10.3390/sym11030347 - 7 Mar 2019
Cited by 96 | Viewed by 3718
Abstract
The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated by several special cases and consequences [...] Read more.
The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated by several special cases and consequences of our main results, which are pointed out herein. Full article
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
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