Toeplitz Determinants for a Certain Family of Analytic Functions Endowed with Borel Distribution

Wanas, Abbas Kareem; Sakar, F. Müge; Oros, Georgia Irina; Cotîrlǎ, Luminiţa-Ioana

doi:10.3390/sym15020262

Cited by 7 publications

(3 citation statements)

References 15 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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“…Recently, Mandal et al [17] determined the best possible bounds for second Hankel and Hermitian Toeplitz matrices, involving logarithmic coefficients of inverse functions, which are applied to starlike and convex functions concerning symmetric points. In recent studies, considerable attention has been devoted to exploring interesting properties associated with Teoplitz and Hankel determinants within the realm of analytic functions of certain classes of convex and starlike functions (see, for example, [18][19][20][21][22][23][24][25][26][27] and references therein). The Toeplitz determinant, characterized by entries corresponding to the logarithmic coefficients of g ∈ S in the form (14), is expressed as…”

Section: Introduction Definitions and Motivationmentioning

confidence: 99%

Sharp Bounds on Toeplitz Determinants for Starlike and Convex Functions Associated with Bilinear Transformations

Sabir

2024

Symmetry

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Starlike and convex functions have gained increased prominence in both academic literature and practical applications over the past decade. Concurrently, logarithmic coefficients play a pivotal role in estimating diverse properties within the realm of analytic functions, whether they are univalent or nonunivalent. In this paper, we rigorously derive bounds for specific Toeplitz determinants involving logarithmic coefficients pertaining to classes of convex and starlike functions concerning symmetric points. Furthermore, we present illustrative examples showcasing the sharpness of these established bounds. Our findings represent a substantial contribution to the advancement of our understanding of logarithmic coefficients and their profound implications across diverse mathematical contexts.

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“…In recent times, a number of researchers have focused on exploring the bounds of the Toeplitz determinant T m (n) for various families of analytic functions (see, for example, [29][30][31][32]). In the investigation of Toeplitz determinants, the research conducted in [33,34] incorporates elements of quantum calculus, while [35] explores a set of analytic functions introduced through the utilization of the Borel distribution.…”

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confidence: 99%

Bounds for Toeplitz Determinants and Related Inequalities for a New Subclass of Analytic Functions

Tang,

Gul,

Hussain

et al. 2023

Mathematics

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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.

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Toeplitz Determinants for a Certain Family of Analytic Functions Endowed with Borel Distribution

Cited by 7 publications

References 15 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

Sharp Bounds on Toeplitz Determinants for Starlike and Convex Functions Associated with Bilinear Transformations

Bounds for Toeplitz Determinants and Related Inequalities for a New Subclass of Analytic Functions

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