Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings
The purpose of this study is to define a new class of harmonically convex functions, which is known as left and right harmonically convex interval-valued function (LR-𝓗-convex <i>IV-F</i>), and to establish novel inclusions for a newly defined class of interval-valued functions (<i>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/4/178 |
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| author | Muhammad Bilal Khan Jorge E. Macías-Díaz Savin Treanțǎ Mohammed S. Soliman Hatim Ghazi Zaini |
| author_facet | Muhammad Bilal Khan Jorge E. Macías-Díaz Savin Treanțǎ Mohammed S. Soliman Hatim Ghazi Zaini |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | The purpose of this study is to define a new class of harmonically convex functions, which is known as left and right harmonically convex interval-valued function (LR-𝓗-convex <i>IV-F</i>), and to establish novel inclusions for a newly defined class of interval-valued functions (<i>IV-Fs)</i> linked to Hermite–Hadamard (<i>H-H</i>) and Hermite–Hadamard–Fejér (<i>H-H</i>-Fejér) type inequalities via interval-valued Riemann–Liouville fractional integrals (<i>IV-RL</i>-fractional integrals). We also attain some related inequalities for the product of two LR-𝓗-convex <i>IV-Fs.</i> These findings enable us to identify a new class of inclusions that may be seen as significant generalizations of results proved by Iscan and Chen. Some examples are included in our findings that may be used to determine the validity of the results. The findings in this work can be seen as a considerable advance over previously published findings. |
| first_indexed | 2024-03-10T04:09:01Z |
| format | Article |
| id | doaj.art-43b0c151374c414982c6d8b795bfe22e |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:09:01Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-43b0c151374c414982c6d8b795bfe22e2023-11-23T08:15:12ZengMDPI AGFractal and Fractional2504-31102022-03-016417810.3390/fractalfract6040178Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued SettingsMuhammad Bilal Khan0Jorge E. Macías-Díaz1Savin Treanțǎ2Mohammed S. Soliman3Hatim Ghazi Zaini4Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, MexicoDepartment of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaDepartment of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaThe purpose of this study is to define a new class of harmonically convex functions, which is known as left and right harmonically convex interval-valued function (LR-𝓗-convex <i>IV-F</i>), and to establish novel inclusions for a newly defined class of interval-valued functions (<i>IV-Fs)</i> linked to Hermite–Hadamard (<i>H-H</i>) and Hermite–Hadamard–Fejér (<i>H-H</i>-Fejér) type inequalities via interval-valued Riemann–Liouville fractional integrals (<i>IV-RL</i>-fractional integrals). We also attain some related inequalities for the product of two LR-𝓗-convex <i>IV-Fs.</i> These findings enable us to identify a new class of inclusions that may be seen as significant generalizations of results proved by Iscan and Chen. Some examples are included in our findings that may be used to determine the validity of the results. The findings in this work can be seen as a considerable advance over previously published findings.https://www.mdpi.com/2504-3110/6/4/178interval-valued functionLR-Harmonically convexityfractional integral operatorHermite–Hadamard type inequalities |
| spellingShingle | Muhammad Bilal Khan Jorge E. Macías-Díaz Savin Treanțǎ Mohammed S. Soliman Hatim Ghazi Zaini Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings Fractal and Fractional interval-valued function LR-Harmonically convexity fractional integral operator Hermite–Hadamard type inequalities |
| title | Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings |
| title_full | Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings |
| title_fullStr | Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings |
| title_full_unstemmed | Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings |
| title_short | Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings |
| title_sort | hermite hadamard inequalities in fractional calculus for left and right harmonically convex functions via interval valued settings |
| topic | interval-valued function LR-Harmonically convexity fractional integral operator Hermite–Hadamard type inequalities |
| url | https://www.mdpi.com/2504-3110/6/4/178 |
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