Generalization of some integral inequalities in multiplicative calculus with their computational analysis
UDC 517.9 We focus on generalizing some multiplicative integral inequalities for twice differentiable functions. First, we derive a multiplicative integral identity for multiplicatively twice differentiable functions. Then, with the help of the integral identit...
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| Date: | 2025 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7765 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512740335943680 |
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| author | Mateen, Abdul Zhang, Zhiyue Ali, Muhammad Aamir Fečkan, Michal Mateen, Abdul Zhang, Zhiyue Ali, Muhammad Aamir Fečkan, Michal |
| author_facet | Mateen, Abdul Zhang, Zhiyue Ali, Muhammad Aamir Fečkan, Michal Mateen, Abdul Zhang, Zhiyue Ali, Muhammad Aamir Fečkan, Michal |
| author_sort | Mateen, Abdul |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-05-09T12:53:50Z |
| description | UDC 517.9
We focus on generalizing some multiplicative integral inequalities for twice differentiable functions. First, we derive a multiplicative integral identity for multiplicatively twice differentiable functions. Then, with the help of the integral identity, we prove a family of integral inequalities, such as Simpson, Hermite–Hadamard, midpoint, trapezoid, and Bullen types inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities to prove the validity  of the results for multiplicatively convex functions. The generalized forms obtained in our research offer valuable tools for researchers in various fields. |
| doi_str_mv | 10.3842/umzh.v76i10.7765 |
| first_indexed | 2026-03-24T03:33:35Z |
| format | Article |
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| id | umjimathkievua-article-7765 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:33:35Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-77652025-05-09T12:53:50Z Generalization of some integral inequalities in multiplicative calculus with their computational analysis Generalization of some integral inequalities in multiplicative calculus with their computational analysis Mateen, Abdul Zhang, Zhiyue Ali, Muhammad Aamir Fečkan, Michal Mateen, Abdul Zhang, Zhiyue Ali, Muhammad Aamir Fečkan, Michal Hermite-Hadamard Inequality, Simpson’s Inequality, Bullen’s Inequality, Multiplicative Calculus, Multiplicatively Convex Function UDC 517.9 We focus on generalizing some multiplicative integral inequalities for twice differentiable functions. First, we derive a multiplicative integral identity for multiplicatively twice differentiable functions. Then, with the help of the integral identity, we prove a family of integral inequalities, such as Simpson, Hermite–Hadamard, midpoint, trapezoid, and Bullen types inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities to prove the validity  of the results for multiplicatively convex functions. The generalized forms obtained in our research offer valuable tools for researchers in various fields. УДК 517.9 Узагальнення деяких інтегральних нерівностей в мультиплікативному численні та їх обчислювальний аналіз Розглянуто узагальнення деяких мультиплікативних інтегральних нерівностей для двічі диференційовних функцій. Спочатку виведено мультиплікативну інтегральну тотожність для мультиплікативно двічі диференційовних функцій. Потім за допомогою інтегральної тотожності доведено серію інтегральних нерівностей, таких як нерівності типу Сімпсона, Ерміта–Адамара, середньої точки, трапеції та Буллена для мультиплікативно опуклих функцій. Крім того, наведено деякі числові приклади та чисельний аналіз цих вперше встановлених нерівностей, щоб довести справедливість результатів для мультиплікативно опуклих функцій. Узагальнені форми, отримані в цій роботі, є цінними інструментами для дослідників у різних областях. Institute of Mathematics, NAS of Ukraine 2025-05-07 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7765 10.3842/umzh.v76i10.7765 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 10 (2024); 1480 - 1496 Український математичний журнал; Том 76 № 10 (2024); 1480 - 1496 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7765/10214 Copyright (c) 2024 Міхал Фечкан |
| spellingShingle | Mateen, Abdul Zhang, Zhiyue Ali, Muhammad Aamir Fečkan, Michal Mateen, Abdul Zhang, Zhiyue Ali, Muhammad Aamir Fečkan, Michal Generalization of some integral inequalities in multiplicative calculus with their computational analysis |
| title | Generalization of some integral inequalities in multiplicative calculus with their computational analysis |
| title_alt | Generalization of some integral inequalities in multiplicative calculus with their computational analysis |
| title_full | Generalization of some integral inequalities in multiplicative calculus with their computational analysis |
| title_fullStr | Generalization of some integral inequalities in multiplicative calculus with their computational analysis |
| title_full_unstemmed | Generalization of some integral inequalities in multiplicative calculus with their computational analysis |
| title_short | Generalization of some integral inequalities in multiplicative calculus with their computational analysis |
| title_sort | generalization of some integral inequalities in multiplicative calculus with their computational analysis |
| topic_facet | Hermite-Hadamard Inequality Simpson’s Inequality Bullen’s Inequality Multiplicative Calculus Multiplicatively Convex Function |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7765 |
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