Hankel and Symmetric Toeplitz Determinants for a New Subclass of q-Starlike Functions

Al-Shbeil, Isra; Gong, Jianhua; Khan, Shahid; Khan, Nazar; Khan, Ajmal; Khan, Mohammad Faisal; Goswami, Anjali

doi:10.3390/fractalfract6110658

Cited by 16 publications

(8 citation statements)

References 35 publications

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“…The estimates for Toeplitz determinants T r (n) for functions in S * q and R, when n and r are small have been studied in Ali et al (2018) , Al-Khafaji et al (2020) , Al-shbeil et al (2022 , Buyankara and Çağlar (2023) , Soh et al (2021) , Radhika et al (2018) , Ramachandran and Kavitha (2017) , Ayinla and Bello (2021) , Rasheed et al (2023) , Sivasubramanian et al (2016) , Srivastava et al (2019) , Tang et al (2023) , Tang et al (2021) , Wahid et al (2022), Wanas et al (2023). Motivated by these results, this study aims to find the determinants of Toeplitz determinants T r (n) for functions in S * q and R q , when n and r are small.…”

Section: Introductionmentioning

confidence: 99%

Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator

Nurali,

Janteng

2024

Sci. Technol. Indones

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An analytic function, also known as a holomorphic function, is a complex-valued function that is differentiable at every point within a given domain. In other words, a function f (z) is analytic in a domain U if it has a derivative f′(z) at every point z in U. Let A represent the set of functions f that are analytic within the open unit disk D = {z ∈ ℂ : |z| < 1}. These functions possess a normalized Taylor-Maclaurin series expansion written in the form f (z) = z + Í∞ n=2 an z n where an ∈ ℂ, n = 2, 3, . . .. In recent years, the field of q-calculus has gained significant attention and research interest among mathematicians. The applications of this field are broadly applied in numerous subdivisions of physics and mathematics. In this research, we assume that S∗q and ℝq are subclasses of analytic functions obtained by applying the q-derivative operator. The objective of this paper is to obtain estimates for coefficient inequalities and Toeplitz determinants whose elements are the coefficients an for f ∈ S∗q and f ∈ Rq .

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Section: Introductionmentioning

confidence: 99%

Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator

Nurali,

Janteng

2024

Sci. Technol. Indones

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“…The second Hankel determinant for specified subsets of bi-univalent functions was investigated by Al-Ameedee et al [25]. The Hankel determinant of m-fold symmetric bi-univalent functions was examined by Atshan et al [26] and other researchers [27][28][29][30] by the utilization of a novel operator. The Hankel determinant of f was investigated by Fekete and Szegö [19] as H 2 (1).…”

Section: Introductionmentioning

confidence: 99%

Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials

Gebur,

Atshan

2024

Symmetry

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Orthogonal polynomials have been widely employed by renowned authors within the context of geometric function theory. This study is driven by prior research and aims to address the —Fekete-Szegö problem. Additionally, we provide bound estimates for the coefficients and an upper bound estimate for the second Hankel determinant for functions belonging to the category of analytical and bi-univalent functions. This investigation incorporates the utilization of Euler polynomials.

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“…Recently, many well-known mathematicians have used q-calculus and studied some subclasses of analytic functions and their properties (see, for example, [8,9]). Recently, several authors published a series of studies [10][11][12] focusing on the classes of q-starlike functions connected to Janowski functions [13] from various angles.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

The Properties of Meromorphic Multivalent q-Starlike Functions in the Janowski Domain

Al-Shbeil

Gong

Ray³

et al. 2023

Fractal Fract

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Many researchers have defined the q-analogous of differential and integral operators for analytic functions using the concept of quantum calculus in the geometric function theory. In this study, we conduct a comprehensive investigation to identify the uses of the Sălăgean q-differential operator for meromorphic multivalent functions. Many features of functions that belong to geometrically defined classes have been extensively studied using differential operators based on q-calculus operator theory. In this research, we extended the idea of the q-analogous of the Sălăgean differential operator for meromorphic multivalent functions using the fundamental ideas of q-calculus. With the help of this operator, we extend the family of Janowski functions by adding two new subclasses of meromorphic q-starlike and meromorphic multivalent q-starlike functions. We discover significant findings for these new classes, including the radius of starlikeness, partial sums, distortion theorems, and coefficient estimates.

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Hankel and Symmetric Toeplitz Determinants for a New Subclass of q-Starlike Functions

Cited by 16 publications

References 35 publications

Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator

Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator

Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials

The Properties of Meromorphic Multivalent q-Starlike Functions in the Janowski Domain

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