A generalization of convexity via an implicit inequality
We unified several kinds of convexity by introducing the class $ \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ of $ (\zeta, w) $-admissible functions $ F: [0, 1]\times I\times I\to \mathbb{R} $. Namely, we proved that most types of convexity from the literature generate functions $ F\in \mathcal{A}_{\z...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024586?viewType=HTML |
| _version_ | 1797216161613479936 |
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| author | Hassen Aydi Bessem Samet Manuel De la Sen |
| author_facet | Hassen Aydi Bessem Samet Manuel De la Sen |
| author_sort | Hassen Aydi |
| collection | DOAJ |
| description | We unified several kinds of convexity by introducing the class $ \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ of $ (\zeta, w) $-admissible functions $ F: [0, 1]\times I\times I\to \mathbb{R} $. Namely, we proved that most types of convexity from the literature generate functions $ F\in \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ for some $ \zeta\in C([0, 1]) $ and $ w\in C^1(I) $ with $ w(I)\subset I $ and $ w' > 0 $. We also studied some properties of $ (\zeta, w) $-admissible functions and established some integral inequalities that unify various Hermite-Hadamard-type inequalities from the literature. |
| first_indexed | 2024-04-24T11:41:34Z |
| format | Article |
| id | doaj.art-58240fb833cd416abf6e4b8733785e49 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T11:41:34Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-58240fb833cd416abf6e4b8733785e492024-04-10T01:17:39ZengAIMS PressAIMS Mathematics2473-69882024-03-0195119921201010.3934/math.2024586A generalization of convexity via an implicit inequalityHassen Aydi 0Bessem Samet1Manuel De la Sen 21. Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia 2. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa3. Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia4. Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940-Leioa (Bizkaia), SpainWe unified several kinds of convexity by introducing the class $ \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ of $ (\zeta, w) $-admissible functions $ F: [0, 1]\times I\times I\to \mathbb{R} $. Namely, we proved that most types of convexity from the literature generate functions $ F\in \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ for some $ \zeta\in C([0, 1]) $ and $ w\in C^1(I) $ with $ w(I)\subset I $ and $ w' > 0 $. We also studied some properties of $ (\zeta, w) $-admissible functions and established some integral inequalities that unify various Hermite-Hadamard-type inequalities from the literature.https://www.aimspress.com/article/doi/10.3934/math.2024586?viewType=HTMLconvexityimplicit inequality$ (\zeta， w) $-admissible functionsintegral inequalitieshermite-hadamard-type inequalities |
| spellingShingle | Hassen Aydi Bessem Samet Manuel De la Sen A generalization of convexity via an implicit inequality AIMS Mathematics convexity implicit inequality $ (\zeta， w) $-admissible functions integral inequalities hermite-hadamard-type inequalities |
| title | A generalization of convexity via an implicit inequality |
| title_full | A generalization of convexity via an implicit inequality |
| title_fullStr | A generalization of convexity via an implicit inequality |
| title_full_unstemmed | A generalization of convexity via an implicit inequality |
| title_short | A generalization of convexity via an implicit inequality |
| title_sort | generalization of convexity via an implicit inequality |
| topic | convexity implicit inequality $ (\zeta， w) $-admissible functions integral inequalities hermite-hadamard-type inequalities |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024586?viewType=HTML |
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