Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator
In this article, we aim to introduce and explore a new class of preinvex functions called $ \mathfrak{n} $-polynomial $ m $-preinvex functions, while also presenting algebraic properties to enhance their numerical significance. We investigate novel variations of Pachpatte and Hermite-Hadamard integr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231306?viewType=HTML |
| _version_ | 1797674884320460800 |
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| author | Muhammad Tariq Asif Ali Shaikh Sotiris K. Ntouyas Jessada Tariboon |
| author_facet | Muhammad Tariq Asif Ali Shaikh Sotiris K. Ntouyas Jessada Tariboon |
| author_sort | Muhammad Tariq |
| collection | DOAJ |
| description | In this article, we aim to introduce and explore a new class of preinvex functions called $ \mathfrak{n} $-polynomial $ m $-preinvex functions, while also presenting algebraic properties to enhance their numerical significance. We investigate novel variations of Pachpatte and Hermite-Hadamard integral inequalities pertaining to the concept of preinvex functions within the framework of the Caputo-Fabrizio fractional integral operator. By utilizing this direction, we establish a novel fractional integral identity that relates to preinvex functions for differentiable mappings of first-order. Furthermore, we derive some novel refinements for Hermite-Hadamard type inequalities for functions whose first-order derivatives are polynomial preinvex in the Caputo-Fabrizio fractional sense. To demonstrate the practical utility of our findings, we present several inequalities using specific real number means. Overall, our investigation sheds light on convex analysis within the context of fractional calculus. |
| first_indexed | 2024-03-11T22:06:39Z |
| format | Article |
| id | doaj.art-23e0ff21e9b443cc9f6d92b7715cdb7d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T22:06:39Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-23e0ff21e9b443cc9f6d92b7715cdb7d2023-09-25T01:40:45ZengAIMS PressAIMS Mathematics2473-69882023-09-01811255722561010.3934/math.20231306Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operatorMuhammad Tariq0Asif Ali Shaikh1Sotiris K. Ntouyas 2Jessada Tariboon31. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan1. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan2. Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece3. Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, ThailandIn this article, we aim to introduce and explore a new class of preinvex functions called $ \mathfrak{n} $-polynomial $ m $-preinvex functions, while also presenting algebraic properties to enhance their numerical significance. We investigate novel variations of Pachpatte and Hermite-Hadamard integral inequalities pertaining to the concept of preinvex functions within the framework of the Caputo-Fabrizio fractional integral operator. By utilizing this direction, we establish a novel fractional integral identity that relates to preinvex functions for differentiable mappings of first-order. Furthermore, we derive some novel refinements for Hermite-Hadamard type inequalities for functions whose first-order derivatives are polynomial preinvex in the Caputo-Fabrizio fractional sense. To demonstrate the practical utility of our findings, we present several inequalities using specific real number means. Overall, our investigation sheds light on convex analysis within the context of fractional calculus.https://www.aimspress.com/article/doi/10.3934/math.20231306?viewType=HTMLconvex functionpreinvex functionhermite-hadamard inequalitypachpatte inequalitycaputo-fabrizio operator |
| spellingShingle | Muhammad Tariq Asif Ali Shaikh Sotiris K. Ntouyas Jessada Tariboon Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator AIMS Mathematics convex function preinvex function hermite-hadamard inequality pachpatte inequality caputo-fabrizio operator |
| title | Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator |
| title_full | Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator |
| title_fullStr | Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator |
| title_full_unstemmed | Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator |
| title_short | Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator |
| title_sort | some novel refinements of hermite hadamard and pachpatte type integral inequalities involving a generalized preinvex function pertaining to caputo fabrizio fractional integral operator |
| topic | convex function preinvex function hermite-hadamard inequality pachpatte inequality caputo-fabrizio operator |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231306?viewType=HTML |
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