Fourth order Hankel determinants for certain subclasses of modified sigmoid-activated analytic functions involving the trigonometric sine function Article Swipe
H. M. Srivastava
,
Nazar Khan
,
Muhtarr A. Bah
,
Ayman Alahmade
,
Ferdous M. O. Tawfiq
,
Zainab Syed
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1186/s13660-024-03150-0
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1186/s13660-024-03150-0
The aim of this paper is to introduce two new subclasses $\mathcal{R}_{\sin }^{m}(\Im )$ and $\mathcal{R}_{\sin }(\Im )$ of analytic functions by making use of subordination involving the sine function and the modified sigmoid activation function $\Im (v)=\frac{2}{1+e^{-v}}$ , $v\geq 0$ in the open unit disc E . Our purpose is to obtain some initial coefficients, Fekete–Szego problems, and upper bounds for the third- and fourth-order Hankel determinants for the functions belonging to these two classes. All the bounds that we will find here are sharp. We also highlight some known consequences of our main results.
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- Language
- en
- Landing Page
- https://doi.org/10.1186/s13660-024-03150-0
- https://journalofinequalitiesandapplications.springeropen.com/counter/pdf/10.1186/s13660-024-03150-0
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- Cited By
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- References
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Fourth order Hankel determinants for certain subclasses of modified sigmoid-activated analytic functions involving the trigonometric sine functionWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-06-14Full publication date if available
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H. M. Srivastava, Nazar Khan, Muhtarr A. Bah, Ayman Alahmade, Ferdous M. O. Tawfiq, Zainab SyedList of authors in order
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https://doi.org/10.1186/s13660-024-03150-0Publisher landing page
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goldOpen access status per OpenAlex
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https://journalofinequalitiesandapplications.springeropen.com/counter/pdf/10.1186/s13660-024-03150-0Direct OA link when available
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Algorithm, Computer scienceTop concepts (fields/topics) attached by OpenAlex
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3Total citation count in OpenAlex
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2025: 3Per-year citation counts (last 5 years)
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| abstract_inverted_index.$v\geq | 83 |
| abstract_inverted_index.Hankel | 116 |
| abstract_inverted_index.bounds | 110, 128 |
| abstract_inverted_index.making | 44 |
| abstract_inverted_index.obtain | 102 |
| abstract_inverted_index.sharp. | 135 |
| abstract_inverted_index.third- | 113 |
| abstract_inverted_index.initial | 104 |
| abstract_inverted_index.purpose | 99 |
| abstract_inverted_index.sigmoid | 55 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.analytic | 41 |
| abstract_inverted_index.classes. | 125 |
| abstract_inverted_index.function | 51, 57 |
| abstract_inverted_index.modified | 54 |
| abstract_inverted_index.results. | 145 |
| abstract_inverted_index.<mml:math | 15, 30, 60, 85 |
| abstract_inverted_index.belonging | 121 |
| abstract_inverted_index.functions | 42, 120 |
| abstract_inverted_index.highlight | 138 |
| abstract_inverted_index.introduce | 8 |
| abstract_inverted_index.involving | 48 |
| abstract_inverted_index.problems, | 107 |
| abstract_inverted_index.}^{m}(\Im | 13 |
| abstract_inverted_index.<mml:mrow> | 69, 74 |
| abstract_inverted_index.<mml:msub> | 32 |
| abstract_inverted_index.<mml:msup> | 72 |
| abstract_inverted_index.activation | 56 |
| abstract_inverted_index.subclasses | 11 |
| abstract_inverted_index.</mml:math> | 25, 39, 81, 90 |
| abstract_inverted_index.</mml:mrow> | 77, 79 |
| abstract_inverted_index.</mml:msub> | 35 |
| abstract_inverted_index.</mml:msup> | 78 |
| abstract_inverted_index.<mml:mfrac> | 67 |
| abstract_inverted_index.</mml:mfrac> | 80 |
| abstract_inverted_index.consequences | 141 |
| abstract_inverted_index.determinants | 117 |
| abstract_inverted_index.fourth-order | 115 |
| abstract_inverted_index.<mml:msubsup> | 17 |
| abstract_inverted_index.coefficients, | 105 |
| abstract_inverted_index.subordination | 47 |
| abstract_inverted_index.</mml:msubsup> | 21 |
| abstract_inverted_index.Fekete–Szego | 106 |
| abstract_inverted_index.$\mathcal{R}_{\sin | 12, 27 |
| abstract_inverted_index.<mml:mi>R</mml:mi> | 18, 33 |
| abstract_inverted_index.<mml:mi>e</mml:mi> | 73 |
| abstract_inverted_index.<mml:mi>m</mml:mi> | 20 |
| abstract_inverted_index.<mml:mi>v</mml:mi> | 64, 76, 87 |
| abstract_inverted_index.<mml:mn>0</mml:mn> | 89 |
| abstract_inverted_index.<mml:mn>1</mml:mn> | 70 |
| abstract_inverted_index.<mml:mn>2</mml:mn> | 68 |
| abstract_inverted_index.<mml:mo>(</mml:mo> | 22, 36, 63 |
| abstract_inverted_index.<mml:mo>)</mml:mo> | 24, 38, 65 |
| abstract_inverted_index.<mml:mo>+</mml:mo> | 71 |
| abstract_inverted_index.<mml:mo>=</mml:mo> | 66 |
| abstract_inverted_index.<mml:mi>ℑ</mml:mi> | 23, 37, 62 |
| abstract_inverted_index.<mml:mo>sin</mml:mo> | 19, 34 |
| abstract_inverted_index.<mml:mo>−</mml:mo> | 75 |
| abstract_inverted_index.<mml:mo>≥</mml:mo> | 88 |
| abstract_inverted_index.(v)=\frac{2}{1+e^{-v}}$ | 59 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML"> | 16, 31, 61, 86 |
| cited_by_percentile_year.max | 97 |
| cited_by_percentile_year.min | 96 |
| corresponding_author_ids | https://openalex.org/A5099131125 |
| countries_distinct_count | 4 |
| institutions_distinct_count | 6 |
| corresponding_institution_ids | https://openalex.org/I176150703 |
| citation_normalized_percentile.value | 0.92981834 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |