On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity
In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, w...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/1/28 |
| _version_ | 1797493930471718912 |
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| author | Tao Yan Ghulam Farid Hafsa Yasmeen Chahn Yong Jung |
| author_facet | Tao Yan Ghulam Farid Hafsa Yasmeen Chahn Yong Jung |
| author_sort | Tao Yan |
| collection | DOAJ |
| description | In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mo>α</mo><mo>,</mo><mi>h</mi><mo>−</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions. |
| first_indexed | 2024-03-10T01:27:03Z |
| format | Article |
| id | doaj.art-a97feede2c774f0d896a643f87c8187f |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T01:27:03Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-a97feede2c774f0d896a643f87c8187f2023-11-23T13:48:53ZengMDPI AGFractal and Fractional2504-31102022-01-01612810.3390/fractalfract6010028On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized ConvexityTao Yan0Ghulam Farid1Hafsa Yasmeen2Chahn Yong Jung3School of Computer Science, Chengdu University, Chengdu 610106, ChinaDepartment of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, PakistanDepartment of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, PakistanDepartment of Business Administration, Gyeongsang National University, Jinju 52828, KoreaIn the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mo>α</mo><mo>,</mo><mi>h</mi><mo>−</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions.https://www.mdpi.com/2504-3110/6/1/28Riemann–Liouville integralshadamard inequality(<i>α</i>,<i>h</i> − <i>m</i>)-convex functionconvex function |
| spellingShingle | Tao Yan Ghulam Farid Hafsa Yasmeen Chahn Yong Jung On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity Fractal and Fractional Riemann–Liouville integrals hadamard inequality (<i>α</i>,<i>h</i> − <i>m</i>)-convex function convex function |
| title | On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity |
| title_full | On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity |
| title_fullStr | On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity |
| title_full_unstemmed | On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity |
| title_short | On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity |
| title_sort | on hadamard type fractional inequalities for riemann liouville integrals via a generalized convexity |
| topic | Riemann–Liouville integrals hadamard inequality (<i>α</i>,<i>h</i> − <i>m</i>)-convex function convex function |
| url | https://www.mdpi.com/2504-3110/6/1/28 |
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