Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex fuzzy-interval-valued functions
To create various kinds of inequalities, the idea of convexity is essential. Convexity and integral inequality hence have a significant link. This study's goals are to introduce a new class of generalized convex fuzzy-interval-valued functions (convex 𝘍𝘐𝘝𝘍s) which are known as (p,J)-convex 𝘍𝘐𝘝𝘍...
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| Format: | Article |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023374?viewType=HTML |
| _version_ | 1811171069025845248 |
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| author | Muhammad Bilal Khan Gustavo Santos-García Hüseyin Budak Savin Treanțǎ Mohamed S. Soliman |
| author_facet | Muhammad Bilal Khan Gustavo Santos-García Hüseyin Budak Savin Treanțǎ Mohamed S. Soliman |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | To create various kinds of inequalities, the idea of convexity is essential. Convexity and integral inequality hence have a significant link. This study's goals are to introduce a new class of generalized convex fuzzy-interval-valued functions (convex 𝘍𝘐𝘝𝘍s) which are known as (p,J)-convex 𝘍𝘐𝘝𝘍s and to establish Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex 𝘍𝘐𝘝𝘍s using fuzzy order relation. The Kulisch-Miranker order relation, which is based on interval space, is used to define this fuzzy order relation level-wise. Additionally, we have demonstrated that, as special examples, our conclusions encompass a sizable class of both new and well-known inequalities for (p,J)-convex 𝘍𝘐𝘝𝘍s. We offer helpful examples that demonstrate the theory created in this study's application. These findings and various methods might point the way in new directions for modeling, interval-valued functions and fuzzy optimization issues. |
| first_indexed | 2024-04-10T17:07:09Z |
| format | Article |
| id | doaj.art-465ecd2762d143869c031cc7cf9384d6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T17:07:09Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-465ecd2762d143869c031cc7cf9384d62023-02-06T01:31:15ZengAIMS PressAIMS Mathematics2473-69882023-01-01837437747010.3934/math.2023374Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex fuzzy-interval-valued functionsMuhammad Bilal Khan0Gustavo Santos-García1Hüseyin Budak 2Savin Treanțǎ 3Mohamed S. Soliman41. Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan2. Facultad de Economía y Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, Spain3. Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey4. Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania5. Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaTo create various kinds of inequalities, the idea of convexity is essential. Convexity and integral inequality hence have a significant link. This study's goals are to introduce a new class of generalized convex fuzzy-interval-valued functions (convex 𝘍𝘐𝘝𝘍s) which are known as (p,J)-convex 𝘍𝘐𝘝𝘍s and to establish Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex 𝘍𝘐𝘝𝘍s using fuzzy order relation. The Kulisch-Miranker order relation, which is based on interval space, is used to define this fuzzy order relation level-wise. Additionally, we have demonstrated that, as special examples, our conclusions encompass a sizable class of both new and well-known inequalities for (p,J)-convex 𝘍𝘐𝘝𝘍s. We offer helpful examples that demonstrate the theory created in this study's application. These findings and various methods might point the way in new directions for modeling, interval-valued functions and fuzzy optimization issues.https://www.aimspress.com/article/doi/10.3934/math.2023374?viewType=HTML(p，j)-convex fuzzy-interval-valued functionfuzzy riemann integraljensen type inequalityschur type inequalityhermite-hadamard type inequalityhermite-hadamard-fejér type inequality |
| spellingShingle | Muhammad Bilal Khan Gustavo Santos-García Hüseyin Budak Savin Treanțǎ Mohamed S. Soliman Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex fuzzy-interval-valued functions AIMS Mathematics (p，j)-convex fuzzy-interval-valued function fuzzy riemann integral jensen type inequality schur type inequality hermite-hadamard type inequality hermite-hadamard-fejér type inequality |
| title | Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex fuzzy-interval-valued functions |
| title_full | Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex fuzzy-interval-valued functions |
| title_fullStr | Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex fuzzy-interval-valued functions |
| title_full_unstemmed | Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex fuzzy-interval-valued functions |
| title_short | Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p,J)-convex fuzzy-interval-valued functions |
| title_sort | some new versions of jensen schur and hermite hadamard type inequalities for p j convex fuzzy interval valued functions |
| topic | (p，j)-convex fuzzy-interval-valued function fuzzy riemann integral jensen type inequality schur type inequality hermite-hadamard type inequality hermite-hadamard-fejér type inequality |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023374?viewType=HTML |
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