New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals
This study uses fuzzy order relations to examine Hermite–Hadamard inequalities (𝐻𝐻-inequalities) for convex fuzzy-number-valued mappings (FNVMs). The Kulisch–Miranker order relation, which is based on interval space, is used to define this fuzzy order relation which is defined level-wise. By utilizi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3251 |
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| author | Muhammad Bilal Khan Gustavo Santos-García Muhammad Aslam Noor Mohamed S. Soliman |
| author_facet | Muhammad Bilal Khan Gustavo Santos-García Muhammad Aslam Noor Mohamed S. Soliman |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | This study uses fuzzy order relations to examine Hermite–Hadamard inequalities (𝐻𝐻-inequalities) for convex fuzzy-number-valued mappings (FNVMs). The Kulisch–Miranker order relation, which is based on interval space, is used to define this fuzzy order relation which is defined level-wise. By utilizing this idea, several novel 𝐻𝐻- and 𝐻𝐻-Fejér-type inequalities are established in the fuzzy environment via convex FNVMs. Additional novel 𝐻𝐻-type inequalities for the product of convex FNVMs are also found and proven with the use of practical examples. Additionally, certain unique situations that can be seen as applications of fuzzy 𝐻𝐻-inequalities are presented. The ideas and methods presented in this work might serve as a springboard for more study in this field. |
| first_indexed | 2024-03-09T23:16:13Z |
| format | Article |
| id | doaj.art-011eed288b9e44c6b54b009abd071697 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:16:13Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-011eed288b9e44c6b54b009abd0716972023-11-23T17:35:19ZengMDPI AGMathematics2227-73902022-09-011018325110.3390/math10183251New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann IntegralsMuhammad Bilal Khan0Gustavo Santos-García1Muhammad Aslam Noor2Mohamed S. Soliman3Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanFacultad de Economía y Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, SpainDepartment of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaThis study uses fuzzy order relations to examine Hermite–Hadamard inequalities (𝐻𝐻-inequalities) for convex fuzzy-number-valued mappings (FNVMs). The Kulisch–Miranker order relation, which is based on interval space, is used to define this fuzzy order relation which is defined level-wise. By utilizing this idea, several novel 𝐻𝐻- and 𝐻𝐻-Fejér-type inequalities are established in the fuzzy environment via convex FNVMs. Additional novel 𝐻𝐻-type inequalities for the product of convex FNVMs are also found and proven with the use of practical examples. Additionally, certain unique situations that can be seen as applications of fuzzy 𝐻𝐻-inequalities are presented. The ideas and methods presented in this work might serve as a springboard for more study in this field.https://www.mdpi.com/2227-7390/10/18/3251fuzzy-number-valued mappingfuzzy Riemann integralconvex fuzzy number valued mappingHermite–Hadamard inequalityHermite–Hadamard–Fejér inequality |
| spellingShingle | Muhammad Bilal Khan Gustavo Santos-García Muhammad Aslam Noor Mohamed S. Soliman New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals Mathematics fuzzy-number-valued mapping fuzzy Riemann integral convex fuzzy number valued mapping Hermite–Hadamard inequality Hermite–Hadamard–Fejér inequality |
| title | New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals |
| title_full | New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals |
| title_fullStr | New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals |
| title_full_unstemmed | New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals |
| title_short | New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals |
| title_sort | new hermite hadamard inequalities for convex fuzzy number valued mappings via fuzzy riemann integrals |
| topic | fuzzy-number-valued mapping fuzzy Riemann integral convex fuzzy number valued mapping Hermite–Hadamard inequality Hermite–Hadamard–Fejér inequality |
| url | https://www.mdpi.com/2227-7390/10/18/3251 |
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