Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus
The importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. The principles of convexity and symmetry are inextricably linked. Because of the...
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022236?viewType=HTML |
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| author | Jorge E. Macías-Díaz Muhammad Bilal Khan Muhammad Aslam Noor Abd Allah A. Mousa Safar M Alghamdi |
| author_facet | Jorge E. Macías-Díaz Muhammad Bilal Khan Muhammad Aslam Noor Abd Allah A. Mousa Safar M Alghamdi |
| author_sort | Jorge E. Macías-Díaz |
| collection | DOAJ |
| description | The importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this study, first, Hermite-Hadamard type inequalities for LR-p-convex interval-valued functions (LR-p-convex-I-V-F) are constructed in this study. Second, for the product of p-convex various Hermite-Hadamard (HH) type integral inequalities are established. Similarly, we also obtain Hermite-Hadamard-Fejér (HH-Fejér) type integral inequality for LR-p-convex-I-V-F. Finally, for LR-p-convex-I-V-F, various discrete Schur's and Jensen's type inequalities are presented. Moreover, the results presented in this study are verified by useful nontrivial examples. Some of the results reported here for be LR-p-convex-I-V-F are generalizations of prior results for convex and harmonically convex functions, as well as p-convex functions. |
| first_indexed | 2024-12-20T18:36:41Z |
| format | Article |
| id | doaj.art-0c0e6ea0679447639043ba2c5295600f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-20T18:36:41Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-0c0e6ea0679447639043ba2c5295600f2022-12-21T19:29:55ZengAIMS PressAIMS Mathematics2473-69882022-01-01734266429210.3934/math.2022236Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculusJorge E. Macías-Díaz0Muhammad Bilal Khan1Muhammad Aslam Noor2Abd Allah A. Mousa3Safar M Alghamdi41. Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico 2. Department of Mathematics, School of Digital Technologies, TallinnUniversity, Narva Rd. 25, 10120 Tallinn, Estonia3. Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan3. Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan4. Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia4. Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaThe importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this study, first, Hermite-Hadamard type inequalities for LR-p-convex interval-valued functions (LR-p-convex-I-V-F) are constructed in this study. Second, for the product of p-convex various Hermite-Hadamard (HH) type integral inequalities are established. Similarly, we also obtain Hermite-Hadamard-Fejér (HH-Fejér) type integral inequality for LR-p-convex-I-V-F. Finally, for LR-p-convex-I-V-F, various discrete Schur's and Jensen's type inequalities are presented. Moreover, the results presented in this study are verified by useful nontrivial examples. Some of the results reported here for be LR-p-convex-I-V-F are generalizations of prior results for convex and harmonically convex functions, as well as p-convex functions.https://www.aimspress.com/article/doi/10.3934/math.2022236?viewType=HTMLinterval-valued functionslr-p-convex interval-valued functionshermite-hadamard type inequality hermite-hadamard-fejér inequalityjensen's type inequalityschur's type inequality |
| spellingShingle | Jorge E. Macías-Díaz Muhammad Bilal Khan Muhammad Aslam Noor Abd Allah A. Mousa Safar M Alghamdi Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus AIMS Mathematics interval-valued functions lr-p-convex interval-valued functions hermite-hadamard type inequality hermite-hadamard-fejér inequality jensen's type inequality schur's type inequality |
| title | Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus |
| title_full | Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus |
| title_fullStr | Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus |
| title_full_unstemmed | Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus |
| title_short | Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus |
| title_sort | hermite hadamard inequalities for generalized convex functions in interval valued calculus |
| topic | interval-valued functions lr-p-convex interval-valued functions hermite-hadamard type inequality hermite-hadamard-fejér inequality jensen's type inequality schur's type inequality |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022236?viewType=HTML |
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