Hermite–Hadamard-Type Inequalities for <i>h</i>-Convex Functions Involving New Fractional Integral Operators with Exponential Kernel
In this paper, we use two new fractional integral operators with exponential kernel about the midpoint of the interval to construct some Hermite–Hadamard type fractional integral inequalities for <i>h</i>-convex functions. Taking two integral identities about the first and second derivat...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/6/309 |
| _version_ | 1797487298097446912 |
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| author | Yaoqun Wu |
| author_facet | Yaoqun Wu |
| author_sort | Yaoqun Wu |
| collection | DOAJ |
| description | In this paper, we use two new fractional integral operators with exponential kernel about the midpoint of the interval to construct some Hermite–Hadamard type fractional integral inequalities for <i>h</i>-convex functions. Taking two integral identities about the first and second derivatives of the function as auxiliary functions, the main results are obtained by using the properties of <i>h</i>-convexity and the module. In order to illustrate the application of the results, we propose four examples and plot function images to intuitively present the meaning of the inequalities in the main results, and we verify the correctness of the conclusion. This study further expands the generalization of Hermite–Hadamard-type inequalities and provides some research references for the study of Hermite–Hadamard-type inequalities. |
| first_indexed | 2024-03-09T23:46:35Z |
| format | Article |
| id | doaj.art-4194e47404b94094bb7b64634bd97758 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T23:46:35Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-4194e47404b94094bb7b64634bd977582023-11-23T16:42:33ZengMDPI AGFractal and Fractional2504-31102022-06-016630910.3390/fractalfract6060309Hermite–Hadamard-Type Inequalities for <i>h</i>-Convex Functions Involving New Fractional Integral Operators with Exponential KernelYaoqun Wu0School of Information Engineering, Shaoyang University, Shaoyang 422000, ChinaIn this paper, we use two new fractional integral operators with exponential kernel about the midpoint of the interval to construct some Hermite–Hadamard type fractional integral inequalities for <i>h</i>-convex functions. Taking two integral identities about the first and second derivatives of the function as auxiliary functions, the main results are obtained by using the properties of <i>h</i>-convexity and the module. In order to illustrate the application of the results, we propose four examples and plot function images to intuitively present the meaning of the inequalities in the main results, and we verify the correctness of the conclusion. This study further expands the generalization of Hermite–Hadamard-type inequalities and provides some research references for the study of Hermite–Hadamard-type inequalities.https://www.mdpi.com/2504-3110/6/6/309fractional integrals operatorsexponential kernelHermite–Hadamard-type inequalities<i>h</i>-convex function |
| spellingShingle | Yaoqun Wu Hermite–Hadamard-Type Inequalities for <i>h</i>-Convex Functions Involving New Fractional Integral Operators with Exponential Kernel Fractal and Fractional fractional integrals operators exponential kernel Hermite–Hadamard-type inequalities <i>h</i>-convex function |
| title | Hermite–Hadamard-Type Inequalities for <i>h</i>-Convex Functions Involving New Fractional Integral Operators with Exponential Kernel |
| title_full | Hermite–Hadamard-Type Inequalities for <i>h</i>-Convex Functions Involving New Fractional Integral Operators with Exponential Kernel |
| title_fullStr | Hermite–Hadamard-Type Inequalities for <i>h</i>-Convex Functions Involving New Fractional Integral Operators with Exponential Kernel |
| title_full_unstemmed | Hermite–Hadamard-Type Inequalities for <i>h</i>-Convex Functions Involving New Fractional Integral Operators with Exponential Kernel |
| title_short | Hermite–Hadamard-Type Inequalities for <i>h</i>-Convex Functions Involving New Fractional Integral Operators with Exponential Kernel |
| title_sort | hermite hadamard type inequalities for i h i convex functions involving new fractional integral operators with exponential kernel |
| topic | fractional integrals operators exponential kernel Hermite–Hadamard-type inequalities <i>h</i>-convex function |
| url | https://www.mdpi.com/2504-3110/6/6/309 |
| work_keys_str_mv | AT yaoqunwu hermitehadamardtypeinequalitiesforihiconvexfunctionsinvolvingnewfractionalintegraloperatorswithexponentialkernel |