On the Grüss type inequalities within $p$-disks with applications
UDC 517.5 We extend the classical Gr\"{u}ss inequality from Euclidean disks in $\mathbb{R}^2$ to generalized $p$-disks and present rigorous formulations for functions satisfying H\"{o}lder-type conditions. Several new Gr\"{u}ss-type inequalities are established and applied...
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| Datum: | 2026 |
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| 1. Verfasser: | |
| 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/6690 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512490829381632 |
|---|---|
| author | Alomari, Mohammad W. Alomari, Mohammad W. |
| author_facet | Alomari, Mohammad W. Alomari, Mohammad W. |
| author_sort | Alomari, Mohammad W. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T11:04:14Z |
| description | UDC 517.5
We extend the classical Gr\"{u}ss inequality from Euclidean disks in $\mathbb{R}^2$ to generalized $p$-disks and present rigorous formulations for functions satisfying H\"{o}lder-type conditions. Several new Gr\"{u}ss-type inequalities are established and applied to establish bounds for the covariance of random variables defined either by probability density functions or by joint distributions. |
| doi_str_mv | 10.3842/umzh.v78i1-2.6690 |
| first_indexed | 2026-03-24T03:29:37Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6690 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:37Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-66902026-03-21T11:04:14Z On the Grüss type inequalities within $p$-disks with applications On the Grüss type inequalities within $p$-disks with applications Alomari, Mohammad W. Alomari, Mohammad W. Gr\ p-circle Generalized Trigonometric Functions Analysis Inequalities Function Teory UDC 517.5 We extend the classical Gr\"{u}ss inequality from Euclidean disks in $\mathbb{R}^2$ to generalized $p$-disks and present rigorous formulations for functions satisfying H\"{o}lder-type conditions. Several new Gr\"{u}ss-type inequalities are established and applied to establish bounds for the covariance of random variables defined either by probability density functions or by joint distributions. УДК 517.5 Про нерівності типу Грюса у $p$-дисках і їхні застосування Розширено класичну нерівність Грюса з евклідових дисків у $\mathbb{R}^2$ на узагальнені $p$-диски та наведено строгі формулювання для функцій, що задовольняють умови типу Гельдера. Доведено кілька нових нерівностей типу Грюса, які застосовано для отримання оцінок коваріації випадкових величин заданих імовірнісними густинами або спільними розподілами. Institute of Mathematics, NAS of Ukraine 2026-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6690 10.3842/umzh.v78i1-2.6690 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 1-2 (2026); 75–76 Український математичний журнал; Том 78 № 1-2 (2026); 75–76 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6690/10618 Copyright (c) 2026 Mohammad W. Alomari |
| spellingShingle | Alomari, Mohammad W. Alomari, Mohammad W. On the Grüss type inequalities within $p$-disks with applications |
| title | On the Grüss type inequalities within $p$-disks with applications |
| title_alt | On the Grüss type inequalities within $p$-disks with applications |
| title_full | On the Grüss type inequalities within $p$-disks with applications |
| title_fullStr | On the Grüss type inequalities within $p$-disks with applications |
| title_full_unstemmed | On the Grüss type inequalities within $p$-disks with applications |
| title_short | On the Grüss type inequalities within $p$-disks with applications |
| title_sort | on the grüss type inequalities within $p$-disks with applications |
| topic_facet | Gr\ p-circle Generalized Trigonometric Functions Analysis Inequalities Function Teory |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6690 |
| work_keys_str_mv | AT alomarimohammadw onthegrusstypeinequalitieswithinpdiskswithapplications AT alomarimohammadw onthegrusstypeinequalitieswithinpdiskswithapplications |