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
Hauptverfasser: Karthikeyan, Kadhavoor R., Lakshmi, Sakkarai, Varadharajan, Seetharam
Format: Artikel
Sprache:Englisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2025
Online Zugang:https://umj.imath.kiev.ua/index.php/umj/article/view/8288
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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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.
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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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