Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator
UDC 517.53 We introduce and study two new subclasses of the function class $\Sigma $ of bi-univalent functions defined in the open unit disk and associated with the Sǎlǎgean and $q$-derivative operators. Furthermore, we find estimates for the Taylor–Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ of...
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| Datum: | 2026 |
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| Format: | Artikel |
| 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/9261 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513453619281920 |
|---|---|
| author | Orhan, Halit Orhan, Halit Orhan, Halit |
| author_facet | Orhan, Halit Orhan, Halit Orhan, Halit |
| author_sort | Orhan, Halit |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T11:04:14Z |
| description | UDC 517.53
We introduce and study two new subclasses of the function class $\Sigma $ of bi-univalent functions defined in the open unit disk and associated with the Sǎlǎgean and $q$-derivative operators. Furthermore, we find estimates for the Taylor–Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ of the functions from these new subclasses. The accumulated results are quite interesting and new. |
| doi_str_mv | 10.3842/umzh.v78i1-2.9261 |
| first_indexed | 2026-03-24T03:44:56Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9261 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:44:56Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-92612026-03-21T11:04:14Z Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator Orhan, Halit Orhan, Halit Orhan, Halit Analytic functions Univalent functions Bi-univalent function Coefficient bounds and coefficient estimates q-derivative operator Salagean derivative operator UDC 517.53 We introduce and study two new subclasses of the function class $\Sigma $ of bi-univalent functions defined in the open unit disk and associated with the Sǎlǎgean and $q$-derivative operators. Furthermore, we find estimates for the Taylor–Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ of the functions from these new subclasses. The accumulated results are quite interesting and new. УДК 517.53 Оцінки коефіцієнтів у нових підкласах аналітичних та бі-унівалентних функцій, визначених комбінаціями $q$-похідної та похідного оператора Сележана Введено та вивчено два нові підкласи класу функцій $\Sigma$ бі-унівалентних функцій, визначених в одиничному колі та пов’язаних з операторами Сележана й $q$-похідної. Одержано оцінки коефіцієнтів Тейлора–Маклорена $|a_{2}|$ і $|a_{3}|$ для функцій із цих нових підкласів. Одержані результати є новими та становлять значний інтерес. Institute of Mathematics, NAS of Ukraine 2026-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9261 10.3842/umzh.v78i1-2.9261 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 1-2 (2026); 88 Український математичний журнал; Том 78 № 1-2 (2026); 88 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9261/10626 Copyright (c) 2026 Halit Orhan |
| spellingShingle | Orhan, Halit Orhan, Halit Orhan, Halit Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator |
| title | Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator |
| title_alt | Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator |
| title_full | Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator |
| title_fullStr | Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator |
| title_full_unstemmed | Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator |
| title_short | Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator |
| title_sort | coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the sǎlǎgean derivative operator |
| topic_facet | Analytic functions Univalent functions Bi-univalent function Coefficient bounds and coefficient estimates q-derivative operator Salagean derivative operator |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9261 |
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