Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators
This study is built on the relationship between inequality theory and fractional analysis. Thanks to the new fractional operators and based on the proportional Caputo-hybrid operators, integral inequalities containing new approaches are obtained for differentiable convex functions. In the findings s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/5/258 |
| _version_ | 1827668890701791232 |
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| author | Mustafa Gürbüz Ahmet Ocak Akdemir Mustafa Ali Dokuyucu |
| author_facet | Mustafa Gürbüz Ahmet Ocak Akdemir Mustafa Ali Dokuyucu |
| author_sort | Mustafa Gürbüz |
| collection | DOAJ |
| description | This study is built on the relationship between inequality theory and fractional analysis. Thanks to the new fractional operators and based on the proportional Caputo-hybrid operators, integral inequalities containing new approaches are obtained for differentiable convex functions. In the findings section, firstly, an integral identity is obtained and various integral inequalities are obtained based on this identity. The peculiarity of the results is that a hybrid operator has been used in inequality theory, which includes the derivative and integral operators together. |
| first_indexed | 2024-03-10T03:51:55Z |
| format | Article |
| id | doaj.art-1d3e8e004c6a4017be406408f788131f |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T03:51:55Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-1d3e8e004c6a4017be406408f788131f2023-11-23T11:03:38ZengMDPI AGFractal and Fractional2504-31102022-05-016525810.3390/fractalfract6050258Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid OperatorsMustafa Gürbüz0Ahmet Ocak Akdemir1Mustafa Ali Dokuyucu2Department of Mathematics Education, Faculty of Education, Aǧri Ibrahim Cecen University, Agri 04100, TurkeyDepartment of Mathematics, Faculty of Science and Letters, Aǧri Ibrahim Cecen University, Agri 04100, TurkeyDepartment of Mathematics, Faculty of Science and Letters, Aǧri Ibrahim Cecen University, Agri 04100, TurkeyThis study is built on the relationship between inequality theory and fractional analysis. Thanks to the new fractional operators and based on the proportional Caputo-hybrid operators, integral inequalities containing new approaches are obtained for differentiable convex functions. In the findings section, firstly, an integral identity is obtained and various integral inequalities are obtained based on this identity. The peculiarity of the results is that a hybrid operator has been used in inequality theory, which includes the derivative and integral operators together.https://www.mdpi.com/2504-3110/6/5/258Hadamard type inequalitiesCaputo derivativethe proportional Caputo-hybrid operator |
| spellingShingle | Mustafa Gürbüz Ahmet Ocak Akdemir Mustafa Ali Dokuyucu Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators Fractal and Fractional Hadamard type inequalities Caputo derivative the proportional Caputo-hybrid operator |
| title | Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators |
| title_full | Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators |
| title_fullStr | Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators |
| title_full_unstemmed | Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators |
| title_short | Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators |
| title_sort | novel approaches for differentiable convex functions via the proportional caputo hybrid operators |
| topic | Hadamard type inequalities Caputo derivative the proportional Caputo-hybrid operator |
| url | https://www.mdpi.com/2504-3110/6/5/258 |
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