Some Certain Fuzzy Fractional Inequalities for Up and Down <em>ℏ</em>-Pre-Invex via Fuzzy-Number Valued Mappings
In this study, we apply a recently developed idea of up and down fuzzy-ordered relations between two fuzzy numbers. Here, we consider fuzzy Riemann–Liouville fractional integrals to establish the Hermite–Hadamard-, Fejér-, and Pachpatte-type inequalities. We estimate fuzzy fractional inequalities fo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/2/171 |
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| author | Muhammad Bilal Khan Adriana Catas Najla Aloraini Mohamed S. Soliman |
| author_facet | Muhammad Bilal Khan Adriana Catas Najla Aloraini Mohamed S. Soliman |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | In this study, we apply a recently developed idea of up and down fuzzy-ordered relations between two fuzzy numbers. Here, we consider fuzzy Riemann–Liouville fractional integrals to establish the Hermite–Hadamard-, Fejér-, and Pachpatte-type inequalities. We estimate fuzzy fractional inequalities for a newly introduced class of <i>ℏ</i>-preinvexity over fuzzy-number valued settings. For the first time, such inequalities involving up and down fuzzy-ordered functions are proven using the fuzzy fractional operator. The stated inequalities are supported by a few numerical examples that will be helpful to validate our main results. |
| first_indexed | 2024-03-11T08:49:01Z |
| format | Article |
| id | doaj.art-931f69e34dd54f3994f2e3eb692d8bc8 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T08:49:01Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-931f69e34dd54f3994f2e3eb692d8bc82023-11-16T20:36:58ZengMDPI AGFractal and Fractional2504-31102023-02-017217110.3390/fractalfract7020171Some Certain Fuzzy Fractional Inequalities for Up and Down <em>ℏ</em>-Pre-Invex via Fuzzy-Number Valued MappingsMuhammad Bilal Khan0Adriana Catas1Najla Aloraini2Mohamed S. Soliman3Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, RomaniaDepartment of Mathematics, College of Sciences and Arts Onaizah, Qassim University, P.O. Box 6640, Buraydah 51452, Saudi ArabiaDepartment of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIn this study, we apply a recently developed idea of up and down fuzzy-ordered relations between two fuzzy numbers. Here, we consider fuzzy Riemann–Liouville fractional integrals to establish the Hermite–Hadamard-, Fejér-, and Pachpatte-type inequalities. We estimate fuzzy fractional inequalities for a newly introduced class of <i>ℏ</i>-preinvexity over fuzzy-number valued settings. For the first time, such inequalities involving up and down fuzzy-ordered functions are proven using the fuzzy fractional operator. The stated inequalities are supported by a few numerical examples that will be helpful to validate our main results.https://www.mdpi.com/2504-3110/7/2/171up and down <i>ℏ</i>-pre-invex fuzzy-interval-valued functionfuzzy Riemann–Liouville fractional integralHermite–Hadamard-type inequalityHermite–Hadamard–Fejér-type inequality |
| spellingShingle | Muhammad Bilal Khan Adriana Catas Najla Aloraini Mohamed S. Soliman Some Certain Fuzzy Fractional Inequalities for Up and Down <em>ℏ</em>-Pre-Invex via Fuzzy-Number Valued Mappings Fractal and Fractional up and down <i>ℏ</i>-pre-invex fuzzy-interval-valued function fuzzy Riemann–Liouville fractional integral Hermite–Hadamard-type inequality Hermite–Hadamard–Fejér-type inequality |
| title | Some Certain Fuzzy Fractional Inequalities for Up and Down <em>ℏ</em>-Pre-Invex via Fuzzy-Number Valued Mappings |
| title_full | Some Certain Fuzzy Fractional Inequalities for Up and Down <em>ℏ</em>-Pre-Invex via Fuzzy-Number Valued Mappings |
| title_fullStr | Some Certain Fuzzy Fractional Inequalities for Up and Down <em>ℏ</em>-Pre-Invex via Fuzzy-Number Valued Mappings |
| title_full_unstemmed | Some Certain Fuzzy Fractional Inequalities for Up and Down <em>ℏ</em>-Pre-Invex via Fuzzy-Number Valued Mappings |
| title_short | Some Certain Fuzzy Fractional Inequalities for Up and Down <em>ℏ</em>-Pre-Invex via Fuzzy-Number Valued Mappings |
| title_sort | some certain fuzzy fractional inequalities for up and down em ℏ em pre invex via fuzzy number valued mappings |
| topic | up and down <i>ℏ</i>-pre-invex fuzzy-interval-valued function fuzzy Riemann–Liouville fractional integral Hermite–Hadamard-type inequality Hermite–Hadamard–Fejér-type inequality |
| url | https://www.mdpi.com/2504-3110/7/2/171 |
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