Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions
Integral inequalities play a crucial role in both theoretical and applied mathematics. Because of the relevance of these notions, we have discussed a new class of introduced generalized convex function called as coordinated left and right convex interval-valued function (coordinated LR-convex IVF) u...
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AIMS Press
2022-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022583?viewType=HTML |
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| author | Muhammad Bilal Khan Hatim Ghazi Zaini Jorge E. Macías-Díaz Savin Treanțǎ Mohamed S. Soliman |
| author_facet | Muhammad Bilal Khan Hatim Ghazi Zaini Jorge E. Macías-Díaz Savin Treanțǎ Mohamed S. Soliman |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | Integral inequalities play a crucial role in both theoretical and applied mathematics. Because of the relevance of these notions, we have discussed a new class of introduced generalized convex function called as coordinated left and right convex interval-valued function (coordinated LR-convex IVF) using the pseudo-order relation (≤p). On interval space, this order relation is defined. First, a pseudo-order relation is used to show Hermite-Hadamard type inequality (HH type inequality) for coordinated LR-convex IVF. Second for coordinated LR-convex IVF, Some HH type inequalities are also derived for the product of two coordinated LR-convex IVFs. Furthermore, we have demonstrated that our conclusions cover a broad range of new and well-known inequalities for coordinated LR-convex IVFs and their variant forms as special instances which are defined by Zhao et al. and Budak et al. Finally, we have shown that the inclusion relation "⊇" confidents to the pseudo-order relation "≤p" for coordinated LR-convex IVFs. The concepts and methodologies presented in this study might serve as a springboard for additional research in this field, as well as a tool for investigating probability and optimization research, among other things. |
| first_indexed | 2024-12-13T17:54:37Z |
| format | Article |
| id | doaj.art-93b7713a61df4770989b887f6ea8eff0 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T17:54:37Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-93b7713a61df4770989b887f6ea8eff02022-12-21T23:36:24ZengAIMS PressAIMS Mathematics2473-69882022-03-0176104541048210.3934/math.2022583Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functionsMuhammad Bilal Khan0Hatim Ghazi Zaini1Jorge E. Macías-Díaz 2Savin Treanțǎ3Mohamed S. Soliman41. Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan2. Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia3. Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico 4. Department of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia5. Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania6. Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIntegral inequalities play a crucial role in both theoretical and applied mathematics. Because of the relevance of these notions, we have discussed a new class of introduced generalized convex function called as coordinated left and right convex interval-valued function (coordinated LR-convex IVF) using the pseudo-order relation (≤p). On interval space, this order relation is defined. First, a pseudo-order relation is used to show Hermite-Hadamard type inequality (HH type inequality) for coordinated LR-convex IVF. Second for coordinated LR-convex IVF, Some HH type inequalities are also derived for the product of two coordinated LR-convex IVFs. Furthermore, we have demonstrated that our conclusions cover a broad range of new and well-known inequalities for coordinated LR-convex IVFs and their variant forms as special instances which are defined by Zhao et al. and Budak et al. Finally, we have shown that the inclusion relation "⊇" confidents to the pseudo-order relation "≤p" for coordinated LR-convex IVFs. The concepts and methodologies presented in this study might serve as a springboard for additional research in this field, as well as a tool for investigating probability and optimization research, among other things.https://www.aimspress.com/article/doi/10.3934/math.2022583?viewType=HTMLcoordinated left and right convex interval-valued functionsdouble interval riemann-liouville-type integralshermite-hadamard type inequalities |
| spellingShingle | Muhammad Bilal Khan Hatim Ghazi Zaini Jorge E. Macías-Díaz Savin Treanțǎ Mohamed S. Soliman Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions AIMS Mathematics coordinated left and right convex interval-valued functions double interval riemann-liouville-type integrals hermite-hadamard type inequalities |
| title | Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions |
| title_full | Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions |
| title_fullStr | Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions |
| title_full_unstemmed | Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions |
| title_short | Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions |
| title_sort | some integral inequalities in interval fractional calculus for left and right coordinated interval valued functions |
| topic | coordinated left and right convex interval-valued functions double interval riemann-liouville-type integrals hermite-hadamard type inequalities |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022583?viewType=HTML |
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