A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators
This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequali...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/4624604 |
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| _version_ | 1849402726984712192 |
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| author | Hasan Kara Hüseyin Budak Sina Etemad Shahram Rezapour Hijaz Ahmad Mohammed K. A. Kaabar |
| author_facet | Hasan Kara Hüseyin Budak Sina Etemad Shahram Rezapour Hijaz Ahmad Mohammed K. A. Kaabar |
| author_sort | Hasan Kara |
| collection | DOAJ |
| description | This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Hölder’s inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained. |
| format | Article |
| id | doaj-art-96cd86ee63134b0a95523c68a17a4ea4 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-96cd86ee63134b0a95523c68a17a4ea42025-08-20T03:37:28ZengWileyJournal of Function Spaces2314-88882023-01-01202310.1155/2023/4624604A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable OperatorsHasan Kara0Hüseyin Budak1Sina Etemad2Shahram Rezapour3Hijaz Ahmad4Mohammed K. A. Kaabar5Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsSection of MathematicsGofa CampThis paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Hölder’s inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained.http://dx.doi.org/10.1155/2023/4624604 |
| spellingShingle | Hasan Kara Hüseyin Budak Sina Etemad Shahram Rezapour Hijaz Ahmad Mohammed K. A. Kaabar A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators Journal of Function Spaces |
| title | A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators |
| title_full | A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators |
| title_fullStr | A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators |
| title_full_unstemmed | A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators |
| title_short | A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators |
| title_sort | study on the new class of inequalities of midpoint type and trapezoidal type based on twice differentiable functions with conformable operators |
| url | http://dx.doi.org/10.1155/2023/4624604 |
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