Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus
UDC 517.5 We define a new class of functions expressed as a convex combination of differential characterizations affected by the multiplicative derivative. Multiplicative derivative is defined in a domain, which excludes zero. Hence, in this case, the defined subclass does not involve replacing the...
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8288 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513019905179648 |
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| author | Karthikeyan, Kadhavoor R. Lakshmi, Sakkarai Varadharajan, Seetharam Karthikeyan, Kadhavoor R. Lakshmi, Sakkarai Varadharajan, Seetharam |
| author_facet | Karthikeyan, Kadhavoor R. Lakshmi, Sakkarai Varadharajan, Seetharam Karthikeyan, Kadhavoor R. Lakshmi, Sakkarai Varadharajan, Seetharam |
| author_sort | Karthikeyan, Kadhavoor R. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-11-05T09:34:46Z |
| description | UDC 517.5
We define a new class of functions expressed as a convex combination of differential characterizations affected by the multiplicative derivative. Multiplicative derivative is defined in a domain, which excludes zero. Hence, in this case, the defined subclass does not involve replacing the ordinary derivative with a multiplicative derivative. However, we have used the motivation behind the purpose of this restrictive calculus given by the circumstances that we have a more versatile calculus of Newton and Euler. Estimates involving the initial coefficients of the functions, which have Maclaurin series and belong to the given function class are our main results. Some examples, along with the graphs, are used to establish the inclusion and the closure properties. Moreover, we obtain the logarithmic and inverse coefficients for the analyzed function class. |
| doi_str_mv | 10.3842/umzh.v77i2.8288 |
| first_indexed | 2026-03-24T03:38:02Z |
| format | Article |
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| id | umjimathkievua-article-8288 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:02Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-82882025-11-05T09:34:46Z Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus Karthikeyan, Kadhavoor R. Lakshmi, Sakkarai Varadharajan, Seetharam Karthikeyan, Kadhavoor R. Lakshmi, Sakkarai Varadharajan, Seetharam univalent function multiplicative calculus starlike Bazilevic subordination Geometric function theory UDC 517.5 We define a new class of functions expressed as a convex combination of differential characterizations affected by the multiplicative derivative. Multiplicative derivative is defined in a domain, which excludes zero. Hence, in this case, the defined subclass does not involve replacing the ordinary derivative with a multiplicative derivative. However, we have used the motivation behind the purpose of this restrictive calculus given by the circumstances that we have a more versatile calculus of Newton and Euler. Estimates involving the initial coefficients of the functions, which have Maclaurin series and belong to the given function class are our main results. Some examples, along with the graphs, are used to establish the inclusion and the closure properties. Moreover, we obtain the logarithmic and inverse coefficients for the analyzed function class. УДК 517.5 Кілька нерівностей для деякого підкласу функцій Базилевича, що включають мультиплікативне числення Розглянуто новий клас функцій, що виражені як опукла комбінація диференціальних характеристик під впливом мультиплікативної похідної. Мультиплікативну похідну визначено в області, яка виключає нуль, і тому підклас, що тут визначено, не передбачає заміни звичайної похідної на мультиплікативну. Саме тому ми використали мотивацію, що стоїть за метою такого обмежуючого числення, враховуючи ту обставину, що ми маємо більш універсальне числення Ньютона та Ейлера. Основними отриманими результатами є оцінки для початкових коефіцієнтів функцій, що мають ряди Маклорена, які належать до визначеного класу функцій. Деякі приклади разом із графіками викорис\-товуються, щоб встановити властивості включення та замикання. Крім того, отримано логарифмічні та обернені коефіцієнти для визначеного класу функцій. Institute of Mathematics, NAS of Ukraine 2025-11-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8288 10.3842/umzh.v77i2.8288 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 2 (2025); 157–158 Український математичний журнал; Том 77 № 2 (2025); 157–158 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8288/10346 Copyright (c) 2025 Kadhavoor R. Karthikeyan, Sakkarai Lakshmi, Seetharam Varadharajan |
| spellingShingle | Karthikeyan, Kadhavoor R. Lakshmi, Sakkarai Varadharajan, Seetharam Karthikeyan, Kadhavoor R. Lakshmi, Sakkarai Varadharajan, Seetharam Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus |
| title | Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus |
| title_alt | Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus |
| title_full | Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus |
| title_fullStr | Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus |
| title_full_unstemmed | Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus |
| title_short | Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus |
| title_sort | some inequalities for a certain subclass of bazilevič functions involving multiplicative calculus |
| topic_facet | univalent function multiplicative calculus starlike Bazilevic subordination Geometric function theory |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8288 |
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