New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals
UDC 517.5 We develop new Hermite–Hadamard-type integral inequalities for $p$-convex functions in the context of $q$-calculus by using the concept of recently defined $T_{q}$-integrals. Then thе obtained Hermite–Hadamard inequality for $p$-convex functions is used to get new Hermite–Hada...
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| Дата: | 2023 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2023
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7200 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512628857634816 |
|---|---|
| author | Gulshan, Ghazala Budak, Hüseyin Hussain, Rashida Ali, Muhammad Aamir Gulshan, Ghazala Budak, Hüseyin Hussain, Rashida Ali, Muhammad Aamir |
| author_facet | Gulshan, Ghazala Budak, Hüseyin Hussain, Rashida Ali, Muhammad Aamir Gulshan, Ghazala Budak, Hüseyin Hussain, Rashida Ali, Muhammad Aamir |
| author_sort | Gulshan, Ghazala |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:34:37Z |
| description | UDC 517.5
We develop new Hermite–Hadamard-type integral inequalities for $p$-convex functions in the context of $q$-calculus by using the concept of recently defined $T_{q}$-integrals. Then thе obtained Hermite–Hadamard inequality for $p$-convex functions is used to get new Hermite–Hadamard inequality for coordinated $p$-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the ideas and techniques of this study may stimulate further research in this field. |
| doi_str_mv | 10.3842/umzh.v75i9.7200 |
| first_indexed | 2026-03-24T03:31:49Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7200 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:49Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-72002024-06-19T00:34:37Z New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals Gulshan, Ghazala Budak, Hüseyin Hussain, Rashida Ali, Muhammad Aamir Gulshan, Ghazala Budak, Hüseyin Hussain, Rashida Ali, Muhammad Aamir Hermite-Hadamard inequality, $p$-convex functions, co-ordinated $p$- convex functions, $_a{T_{q}}$-integral, $^b{T_{q}}$ integral. UDC 517.5 We develop new Hermite–Hadamard-type integral inequalities for $p$-convex functions in the context of $q$-calculus by using the concept of recently defined $T_{q}$-integrals. Then thе obtained Hermite–Hadamard inequality for $p$-convex functions is used to get new Hermite–Hadamard inequality for coordinated $p$-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the ideas and techniques of this study may stimulate further research in this field. УДК 517.5 Нові квантові нерівності Ерміта–Адамара для $p$-опуклих функцій, що включають нещодавно визначені квантові інтеграли Основною метою цього дослідження є розробка нових інтегральних нерівностей типу Ерміта–Адамара для $p$-опуклих функцій в контексті $q$-числення за допомогою концепції $T_{q}$- інтегралів, що були нещодавно визначені. Далі отриману нерівність Ерміта–Адамара для $p$-опуклих функцій використано для виведення нової нерівності Ерміта–Адамара для координованих $p$-опуклих функцій. Крім того, наведено кілька прикладів, щоб продемонструвати достовірність отриманих основних результатів. Ми сподіваємося, що ідеї та методи, запропоновані в цій роботі, можуть стимулювати подальші дослідження в цій галузі. Institute of Mathematics, NAS of Ukraine 2023-09-26 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7200 10.3842/umzh.v75i9.7200 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 9 (2023); 1204 - 1219 Український математичний журнал; Том 75 № 9 (2023); 1204 - 1219 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7200/9747 Copyright (c) 2023 Hüseyin Budak |
| spellingShingle | Gulshan, Ghazala Budak, Hüseyin Hussain, Rashida Ali, Muhammad Aamir Gulshan, Ghazala Budak, Hüseyin Hussain, Rashida Ali, Muhammad Aamir New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals |
| title | New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals |
| title_alt | New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals |
| title_full | New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals |
| title_fullStr | New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals |
| title_full_unstemmed | New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals |
| title_short | New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals |
| title_sort | new quantum hermite–hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals |
| topic_facet | Hermite-Hadamard inequality $p$-convex functions co-ordinated $p$- convex functions $_a{T_{q}}$-integral $^b{T_{q}}$ integral. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7200 |
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