Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities
In this paper, we discuss the Riemann–Liouville fractional integral operator for left and right convex interval-valued functions (left and right convex <i>I∙V</i><i>-</i><i>F</i>), as well as various related notions and concepts. First, the authors used the Rieman...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/2/341 |
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| author | Muhammad Bilal Khan Hatim Ghazi Zaini Savin Treanțǎ Gustavo Santos-García Jorge E. Macías-Díaz Mohamed S. Soliman |
| author_facet | Muhammad Bilal Khan Hatim Ghazi Zaini Savin Treanțǎ Gustavo Santos-García Jorge E. Macías-Díaz Mohamed S. Soliman |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | In this paper, we discuss the Riemann–Liouville fractional integral operator for left and right convex interval-valued functions (left and right convex <i>I∙V</i><i>-</i><i>F</i>), as well as various related notions and concepts. First, the authors used the Riemann–Liouville fractional integral to prove Hermite–Hadamard type (𝓗–𝓗 type) inequality. Furthermore, 𝓗–𝓗 type inequalities for the product of two left and right convex <i>I∙V</i><i>-</i><i>Fs</i> have been established. Finally, for left and right convex <i>I∙V</i><i>-</i><i>Fs</i>, we found the Riemann–Liouville fractional integral Hermite–Hadamard type inequality (𝓗–𝓗 Fejér type inequality). The findings of this research show that this methodology may be applied directly and is computationally simple and precise. |
| first_indexed | 2024-03-09T20:57:39Z |
| format | Article |
| id | doaj.art-9d6f73b3611843dc94a7a811225e2056 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T20:57:39Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9d6f73b3611843dc94a7a811225e20562023-11-23T22:17:01ZengMDPI AGSymmetry2073-89942022-02-0114234110.3390/sym14020341Fractional Calculus for Convex Functions in Interval-Valued Settings and InequalitiesMuhammad Bilal Khan0Hatim Ghazi Zaini1Savin Treanțǎ2Gustavo Santos-García3Jorge E. Macías-Díaz4Mohamed S. Soliman5Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaFacultad de Economía y Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, SpainDepartamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, MexicoDepartment of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIn this paper, we discuss the Riemann–Liouville fractional integral operator for left and right convex interval-valued functions (left and right convex <i>I∙V</i><i>-</i><i>F</i>), as well as various related notions and concepts. First, the authors used the Riemann–Liouville fractional integral to prove Hermite–Hadamard type (𝓗–𝓗 type) inequality. Furthermore, 𝓗–𝓗 type inequalities for the product of two left and right convex <i>I∙V</i><i>-</i><i>Fs</i> have been established. Finally, for left and right convex <i>I∙V</i><i>-</i><i>Fs</i>, we found the Riemann–Liouville fractional integral Hermite–Hadamard type inequality (𝓗–𝓗 Fejér type inequality). The findings of this research show that this methodology may be applied directly and is computationally simple and precise.https://www.mdpi.com/2073-8994/14/2/341left and right convex interval-valued functionfractional integral operatorHermite–Hadamard type inequalityHermite–Hadamard Fejér type inequality |
| spellingShingle | Muhammad Bilal Khan Hatim Ghazi Zaini Savin Treanțǎ Gustavo Santos-García Jorge E. Macías-Díaz Mohamed S. Soliman Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities Symmetry left and right convex interval-valued function fractional integral operator Hermite–Hadamard type inequality Hermite–Hadamard Fejér type inequality |
| title | Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities |
| title_full | Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities |
| title_fullStr | Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities |
| title_full_unstemmed | Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities |
| title_short | Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities |
| title_sort | fractional calculus for convex functions in interval valued settings and inequalities |
| topic | left and right convex interval-valued function fractional integral operator Hermite–Hadamard type inequality Hermite–Hadamard Fejér type inequality |
| url | https://www.mdpi.com/2073-8994/14/2/341 |
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