On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and Applications
In this study, we apply fractional calculus on certain convex functions and derive many novel mean-type inequalities by employing fractional calculus and convexity theory. In order to investigate fractional mean inequalities, we first build an identity in this study. Then, with its help, we derive m...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/5/345 |
| _version_ | 1797599994053656576 |
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| author | Miguel Vivas-Cortez Muzammil Mukhtar Iram Shabbir Muhammad Samraiz Muhammad Yaqoob |
| author_facet | Miguel Vivas-Cortez Muzammil Mukhtar Iram Shabbir Muhammad Samraiz Muhammad Yaqoob |
| author_sort | Miguel Vivas-Cortez |
| collection | DOAJ |
| description | In this study, we apply fractional calculus on certain convex functions and derive many novel mean-type inequalities by employing fractional calculus and convexity theory. In order to investigate fractional mean inequalities, we first build an identity in this study. Then, with its help, we derive many mean-type inequalities and estimate the error of HH inequality using a generalized version of RL-fractional integrals and certain classes of convex functions. The results obtained are validated by taking specific functions. Many mean-type inequalities that exist in the literature are generalized by the main results of this study. |
| first_indexed | 2024-03-11T03:43:15Z |
| format | Article |
| id | doaj.art-00bf64267e114c0fb5acf1415acc3e94 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T03:43:15Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-00bf64267e114c0fb5acf1415acc3e942023-11-18T01:25:47ZengMDPI AGFractal and Fractional2504-31102023-04-017534510.3390/fractalfract7050345On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and ApplicationsMiguel Vivas-Cortez0Muzammil Mukhtar1Iram Shabbir2Muhammad Samraiz3Muhammad Yaqoob4Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Av. 12 de octubre 1076, Apartado, Quito 17-01-2184, EcuadorDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalnagar 62300, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalnagar 62300, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalnagar 62300, PakistanIn this study, we apply fractional calculus on certain convex functions and derive many novel mean-type inequalities by employing fractional calculus and convexity theory. In order to investigate fractional mean inequalities, we first build an identity in this study. Then, with its help, we derive many mean-type inequalities and estimate the error of HH inequality using a generalized version of RL-fractional integrals and certain classes of convex functions. The results obtained are validated by taking specific functions. Many mean-type inequalities that exist in the literature are generalized by the main results of this study.https://www.mdpi.com/2504-3110/7/5/345mean inequalitiesfractional integralHölder’s inequalityMinkowski inequality |
| spellingShingle | Miguel Vivas-Cortez Muzammil Mukhtar Iram Shabbir Muhammad Samraiz Muhammad Yaqoob On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and Applications Fractal and Fractional mean inequalities fractional integral Hölder’s inequality Minkowski inequality |
| title | On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and Applications |
| title_full | On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and Applications |
| title_fullStr | On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and Applications |
| title_full_unstemmed | On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and Applications |
| title_short | On Fractional Integral Inequalities of Riemann Type for Composite Convex Functions and Applications |
| title_sort | on fractional integral inequalities of riemann type for composite convex functions and applications |
| topic | mean inequalities fractional integral Hölder’s inequality Minkowski inequality |
| url | https://www.mdpi.com/2504-3110/7/5/345 |
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