On a modified version of Jensen inequality
<p/> <p>The right-hand side of the Jensen inequality is multiplied by a constant and the related equation is considered. It is shown that every continuous solution of this equation is of the form <inline-formula><graphic file="1029-242X-1999-120505-i1.gif"/></inl...
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| Format: | Article |
| Language: | English |
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SpringerOpen
1999-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/3/120505 |
| _version_ | 1819041529180717056 |
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| author | Szostok Tomasz |
| author_facet | Szostok Tomasz |
| author_sort | Szostok Tomasz |
| collection | DOAJ |
| description | <p/> <p>The right-hand side of the Jensen inequality is multiplied by a constant and the related equation is considered. It is shown that every continuous solution of this equation is of the form <inline-formula><graphic file="1029-242X-1999-120505-i1.gif"/></inline-formula> for some <inline-formula><graphic file="1029-242X-1999-120505-i2.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-1999-120505-i3.gif"/></inline-formula>. Further, it is proved that some functions satisfying the inequality considered are bounded below but not above by suitable solutions of the corresponding equation.</p> |
| first_indexed | 2024-12-21T09:26:26Z |
| format | Article |
| id | doaj.art-68c62edb7a7d4fb1a518053b2b0d9160 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-21T09:26:26Z |
| publishDate | 1999-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-68c62edb7a7d4fb1a518053b2b0d91602022-12-21T19:08:53ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1999-01-0119994120505On a modified version of Jensen inequalitySzostok Tomasz<p/> <p>The right-hand side of the Jensen inequality is multiplied by a constant and the related equation is considered. It is shown that every continuous solution of this equation is of the form <inline-formula><graphic file="1029-242X-1999-120505-i1.gif"/></inline-formula> for some <inline-formula><graphic file="1029-242X-1999-120505-i2.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-1999-120505-i3.gif"/></inline-formula>. Further, it is proved that some functions satisfying the inequality considered are bounded below but not above by suitable solutions of the corresponding equation.</p>http://www.journalofinequalitiesandapplications.com/content/3/120505Jensen's inequalityFunctional inequalityA corresponding functional equation |
| spellingShingle | Szostok Tomasz On a modified version of Jensen inequality Journal of Inequalities and Applications Jensen's inequality Functional inequality A corresponding functional equation |
| title | On a modified version of Jensen inequality |
| title_full | On a modified version of Jensen inequality |
| title_fullStr | On a modified version of Jensen inequality |
| title_full_unstemmed | On a modified version of Jensen inequality |
| title_short | On a modified version of Jensen inequality |
| title_sort | on a modified version of jensen inequality |
| topic | Jensen's inequality Functional inequality A corresponding functional equation |
| url | http://www.journalofinequalitiesandapplications.com/content/3/120505 |
| work_keys_str_mv | AT szostoktomasz onamodifiedversionofjenseninequality |