On an Inequality of H. G. Hardy
<p/> <p>We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/264347 |
| _version_ | 1818039395280748544 |
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| author | Krulić Kristina Iqbal Sajid Pečarić Josip |
| author_facet | Krulić Kristina Iqbal Sajid Pečarić Josip |
| author_sort | Krulić Kristina |
| collection | DOAJ |
| description | <p/> <p>We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as well as fractional integrals of a function with respect to another function. Finally, we apply our main result to multidimensional settings to obtain new results involving mixed Riemann-Liouville fractional integrals.</p> |
| first_indexed | 2024-12-10T07:57:57Z |
| format | Article |
| id | doaj.art-f53f220ff30741419a819e8e4fe9b906 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-10T07:57:57Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-f53f220ff30741419a819e8e4fe9b9062022-12-22T01:56:51ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-0120101264347On an Inequality of H. G. HardyKrulić KristinaIqbal SajidPečarić Josip<p/> <p>We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as well as fractional integrals of a function with respect to another function. Finally, we apply our main result to multidimensional settings to obtain new results involving mixed Riemann-Liouville fractional integrals.</p>http://www.journalofinequalitiesandapplications.com/content/2010/264347 |
| spellingShingle | Krulić Kristina Iqbal Sajid Pečarić Josip On an Inequality of H. G. Hardy Journal of Inequalities and Applications |
| title | On an Inequality of H. G. Hardy |
| title_full | On an Inequality of H. G. Hardy |
| title_fullStr | On an Inequality of H. G. Hardy |
| title_full_unstemmed | On an Inequality of H. G. Hardy |
| title_short | On an Inequality of H. G. Hardy |
| title_sort | on an inequality of h g hardy |
| url | http://www.journalofinequalitiesandapplications.com/content/2010/264347 |
| work_keys_str_mv | AT kruli263kristina onaninequalityofhghardy AT iqbalsajid onaninequalityofhghardy AT pe269ari263josip onaninequalityofhghardy |