New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions
This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, H\"{o}lder's inequality, and the power-mean inequality,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2024-03-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/3564183 |
| _version_ | 1827283872555991040 |
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| author | Hasan Kara Henok Desalegn Desta Hüseyin Budak |
| author_facet | Hasan Kara Henok Desalegn Desta Hüseyin Budak |
| author_sort | Hasan Kara |
| collection | DOAJ |
| description | This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, H\"{o}lder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples. |
| first_indexed | 2024-04-24T09:44:30Z |
| format | Article |
| id | doaj.art-7f08c834a3f74ef78e61883ae2aace3b |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-04-24T09:44:30Z |
| publishDate | 2024-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-7f08c834a3f74ef78e61883ae2aace3b2024-04-15T04:06:04ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532024-03-0171303710.32323/ujma.13970511225New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable FunctionsHasan Kara0Henok Desalegn Desta1Hüseyin Budak2DUZCE UNIVERSITYHaramaya UniversityDUZCE UNIVERSITYThis paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, H\"{o}lder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples.https://dergipark.org.tr/tr/download/article-file/3564183convex functionfractional integralsmilne type inequalitiestwice differentiable |
| spellingShingle | Hasan Kara Henok Desalegn Desta Hüseyin Budak New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions Universal Journal of Mathematics and Applications convex function fractional integrals milne type inequalities twice differentiable |
| title | New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions |
| title_full | New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions |
| title_fullStr | New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions |
| title_full_unstemmed | New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions |
| title_short | New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions |
| title_sort | new perspectives on fractional milne type inequalities insights from twice differentiable functions |
| topic | convex function fractional integrals milne type inequalities twice differentiable |
| url | https://dergipark.org.tr/tr/download/article-file/3564183 |
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