Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals
In the paper, based on Erdélyi-Kober fractional integrals $ ^\rho \mathcal{K}^\alpha_{\chi+}f $ and $ ^\rho \mathcal{K}^\alpha_{\chi-}f $ for any $ \chi\in[a, b] $ with $ f\in\mathfrak{X}_c^p(a, b) $, authors establish some new Hermite-Hadamard type inequalities for convex function. The obtained ine...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2021-08-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021666?viewType=HTML |
| _version_ | 1818914605896826880 |
|---|---|
| author | XuRan Hai ShuHong Wang |
| author_facet | XuRan Hai ShuHong Wang |
| author_sort | XuRan Hai |
| collection | DOAJ |
| description | In the paper, based on Erdélyi-Kober fractional integrals $ ^\rho \mathcal{K}^\alpha_{\chi+}f $ and $ ^\rho \mathcal{K}^\alpha_{\chi-}f $ for any $ \chi\in[a, b] $ with $ f\in\mathfrak{X}_c^p(a, b) $, authors establish some new Hermite-Hadamard type inequalities for convex function. The obtained inequalities generalize the corresponding results for Riemann-Liouville fractional integrals by taking limits when a parameter $ \rho\rightarrow1 $. As applications, the error estimations of Hermite-Hadamard type inequality are also provided. |
| first_indexed | 2024-12-19T23:49:03Z |
| format | Article |
| id | doaj.art-c256bf33d7534e6199e61b874859c690 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-19T23:49:03Z |
| publishDate | 2021-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c256bf33d7534e6199e61b874859c6902022-12-21T20:01:13ZengAIMS PressAIMS Mathematics2473-69882021-08-01610114941150710.3934/math.2021666Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integralsXuRan Hai0ShuHong Wang1College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao 028000, ChinaCollege of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao 028000, ChinaIn the paper, based on Erdélyi-Kober fractional integrals $ ^\rho \mathcal{K}^\alpha_{\chi+}f $ and $ ^\rho \mathcal{K}^\alpha_{\chi-}f $ for any $ \chi\in[a, b] $ with $ f\in\mathfrak{X}_c^p(a, b) $, authors establish some new Hermite-Hadamard type inequalities for convex function. The obtained inequalities generalize the corresponding results for Riemann-Liouville fractional integrals by taking limits when a parameter $ \rho\rightarrow1 $. As applications, the error estimations of Hermite-Hadamard type inequality are also provided.https://www.aimspress.com/article/doi/10.3934/math.2021666?viewType=HTMLhermite-hadamard inequalityconvex functionerdélyi-kober fractional integralsriemann-liouville fractional integralserror estimations |
| spellingShingle | XuRan Hai ShuHong Wang Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals AIMS Mathematics hermite-hadamard inequality convex function erdélyi-kober fractional integrals riemann-liouville fractional integrals error estimations |
| title | Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals |
| title_full | Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals |
| title_fullStr | Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals |
| title_full_unstemmed | Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals |
| title_short | Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals |
| title_sort | hermite hadamard type inequalities based on the erdelyi kober fractional integrals |
| topic | hermite-hadamard inequality convex function erdélyi-kober fractional integrals riemann-liouville fractional integrals error estimations |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021666?viewType=HTML |
| work_keys_str_mv | AT xuranhai hermitehadamardtypeinequalitiesbasedontheerdelyikoberfractionalintegrals AT shuhongwang hermitehadamardtypeinequalitiesbasedontheerdelyikoberfractionalintegrals |