Toeplitz Determinants for the Class of Functions with Bounded Turning

Wahid, Nur; Mohamad, Dzulkifli; Kamarozzaman, Nur Maziah; Shahminan, Ainurraziqin Ahamad

doi:10.29020/nybg.ejpam.v15i4.4559

Cited by 2 publications

(1 citation statement)

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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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