Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator
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...
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| Format: | Article |
| Language: | English |
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Magister Program of Material Sciences, Graduate School of Universitas Sriwijaya
2024-04-01
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| Series: | Science and Technology Indonesia |
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| Online Access: | https://sciencetechindonesia.com/index.php/jsti/article/view/865 |
| _version_ | 1797221965236273152 |
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| author | Nurdiana Binti Nurali Aini Janteng |
| author_facet | Nurdiana Binti Nurali Aini Janteng |
| author_sort | Nurdiana Binti Nurali |
| collection | DOAJ |
| description | 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 . |
| first_indexed | 2024-04-24T13:13:49Z |
| format | Article |
| id | doaj.art-5487bf6d06a74d68993b23784cf251b4 |
| institution | Directory Open Access Journal |
| issn | 2580-4405 2580-4391 |
| language | English |
| last_indexed | 2024-04-24T13:13:49Z |
| publishDate | 2024-04-01 |
| publisher | Magister Program of Material Sciences, Graduate School of Universitas Sriwijaya |
| record_format | Article |
| series | Science and Technology Indonesia |
| spelling | doaj.art-5487bf6d06a74d68993b23784cf251b42024-04-04T23:39:38ZengMagister Program of Material Sciences, Graduate School of Universitas SriwijayaScience and Technology Indonesia2580-44052580-43912024-04-019235435810.26554/sti.2024.9.2.354-358815Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative OperatorNurdiana Binti Nurali0Aini Janteng1Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Kota Kinabalu, Sabah, 88450, MalaysiaFaculty of Science and Natural Resources, Universiti Malaysia Sabah, Kota Kinabalu, Sabah, 88450, MalaysiaAn 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 .https://sciencetechindonesia.com/index.php/jsti/article/view/865analytic functionstoeplitz determinantquantum (or q-) calculusq-derivative operator |
| spellingShingle | Nurdiana Binti Nurali Aini Janteng Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator Science and Technology Indonesia analytic functions toeplitz determinant quantum (or q-) calculus q-derivative operator |
| title | Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator |
| title_full | Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator |
| title_fullStr | Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator |
| title_full_unstemmed | Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator |
| title_short | Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator |
| title_sort | results on toeplitz determinants for subclasses of analytic functions associated to q derivative operator |
| topic | analytic functions toeplitz determinant quantum (or q-) calculus q-derivative operator |
| url | https://sciencetechindonesia.com/index.php/jsti/article/view/865 |
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