New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals
In this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal se...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/4/568 |
| _version_ | 1797571368762474496 |
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| author | Ohud Almutairi Adem Kılıçman |
| author_facet | Ohud Almutairi Adem Kılıçman |
| author_sort | Ohud Almutairi |
| collection | DOAJ |
| description | In this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. This fractional integral generalizes Riemann-Liouville and Hadamard’s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality. |
| first_indexed | 2024-03-10T20:39:25Z |
| format | Article |
| id | doaj.art-00d7bfbc4b3f470693e8b6f2bd574032 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:39:25Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-00d7bfbc4b3f470693e8b6f2bd5740322023-11-19T20:45:13ZengMDPI AGSymmetry2073-89942020-04-0112456810.3390/sym12040568New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional IntegralsOhud Almutairi0Adem Kılıçman1Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi ArabiaDepartment of Mathematics and Institite for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, MalaysiaIn this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. This fractional integral generalizes Riemann-Liouville and Hadamard’s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality.https://www.mdpi.com/2073-8994/12/4/568convex functiongeneralized convex functionHermite–Hadamard inequalityKatugampola fractional integral |
| spellingShingle | Ohud Almutairi Adem Kılıçman New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals Symmetry convex function generalized convex function Hermite–Hadamard inequality Katugampola fractional integral |
| title | New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals |
| title_full | New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals |
| title_fullStr | New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals |
| title_full_unstemmed | New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals |
| title_short | New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals |
| title_sort | new generalized hermite hadamard inequality and related integral inequalities involving katugampola type fractional integrals |
| topic | convex function generalized convex function Hermite–Hadamard inequality Katugampola fractional integral |
| url | https://www.mdpi.com/2073-8994/12/4/568 |
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