Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function
UDC 517.5 We determine the sharp bound of the second-order Hankel determinant $H_{2,2}(f)$ and the coefficient functional for functions from the class of $q$-starlike functions $ \mathcal{S}^*(\mathcal{L},q)$ by refining the results obtained in [Srivastava et al., Upper bound of the third Hankel de...
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| Datum: | 2026 |
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| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9106 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513381306335232 |
|---|---|
| author | Kumar, Karri Sanjay Kumar, Karri Sanjay |
| author_facet | Kumar, Karri Sanjay Kumar, Karri Sanjay |
| author_sort | Kumar, Karri Sanjay |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:36:21Z |
| description | UDC 517.5
We determine the sharp bound of the second-order Hankel determinant $H_{2,2}(f)$ and the coefficient functional for functions from the class of $q$-starlike functions $ \mathcal{S}^*(\mathcal{L},q)$ by refining the results obtained in [Srivastava et al., Upper bound of the third Hankel determinant for a subclass of $q$-starlike functions associated with the $q$-exponential function, Bull. Sci. Math., 167 (2021); https://doi.org/10.1016/j.bulsci.2020.102942]. Moreover, we obtain sharp estimates for the Fekete–Szegö functional and the coefficient differences for the analyzed class of functions. |
| doi_str_mv | 10.3842/umzh.v77i12.9106 |
| first_indexed | 2026-03-24T03:43:46Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9106 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:43:46Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-91062026-03-21T13:36:21Z Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function Kumar, Karri Sanjay Kumar, Karri Sanjay Analytic functions q-derivative Hankel determinant q starlike functions q-exponential function. 30C45 30C50 UDC 517.5 We determine the sharp bound of the second-order Hankel determinant $H_{2,2}(f)$ and the coefficient functional for functions from the class of $q$-starlike functions $ \mathcal{S}^*(\mathcal{L},q)$ by refining the results obtained in [Srivastava et al., Upper bound of the third Hankel determinant for a subclass of $q$-starlike functions associated with the $q$-exponential function, Bull. Sci. Math., 167 (2021); https://doi.org/10.1016/j.bulsci.2020.102942]. Moreover, we obtain sharp estimates for the Fekete–Szegö functional and the coefficient differences for the analyzed class of functions. УДК 517.5 Точна межа для другого визначника Ганкеля для $q$-зіркоподібної функції, пов'язаної з $q$-експоненціальною функцією Досліджено точну межу визначника Ганкеля $H_{2,2}(f)$ другого порядку та коефіцієнтного функціонала для функцій, що належать до класу $q$-зіркоподібних функцій $\mathcal{S}^*(\mathcal{L},q)$. Ці результати отримано шляхом уточнення теорем, наведених у праці Шрівастави та ін. [Upper bound of the third Hankel determinant for a subclass of $q$-starlike functions associated with the $q$-exponential function, Bull. Sci. Math., 167 (2021); https://doi.org/10.1016/j.bulsci.2020.102942]. Також отримано точні оцінки для функціонала Фекете–Сеге та різниць коефіцієнтів у визначеному класі функцій. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9106 10.3842/umzh.v77i12.9106 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 12 (2025); 745 Український математичний журнал; Том 77 № 12 (2025); 745 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9106/10610 Copyright (c) 2025 Karri Sanjay Kumar |
| spellingShingle | Kumar, Karri Sanjay Kumar, Karri Sanjay Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function |
| title | Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function |
| title_alt | Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function |
| title_full | Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function |
| title_fullStr | Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function |
| title_full_unstemmed | Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function |
| title_short | Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function |
| title_sort | sharp bound for the second hankel determinant for a $q$-starlike function associated with the $q$-exponential function |
| topic_facet | Analytic functions q-derivative Hankel determinant q starlike functions q-exponential function. 30C45 30C50 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9106 |
| work_keys_str_mv | AT kumarkarrisanjay sharpboundforthesecondhankeldeterminantforaqstarlikefunctionassociatedwiththeqexponentialfunction AT kumarkarrisanjay sharpboundforthesecondhankeldeterminantforaqstarlikefunctionassociatedwiththeqexponentialfunction |