Some new fractal Milne-type integral inequalities via generalized convexity with applications
This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set. To that end, we develop a novel generalized integral identity involving first-order generalized derivatives. Finally, as applications,...
| Main Authors: | , , , |
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| Format: | Article |
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Multidisciplinary Digital Publishing Institute
2023
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| _version_ | 1811137894383878144 |
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| author | Meftah, Badreddine Lakhdari, Abdelghani Saleh, Wedad Kilicman, Adem |
| author_facet | Meftah, Badreddine Lakhdari, Abdelghani Saleh, Wedad Kilicman, Adem |
| author_sort | Meftah, Badreddine |
| collection | UPM |
| description | This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set. To that end, we develop a novel generalized integral identity involving first-order generalized derivatives. Finally, as applications, some error estimates for the Milne-type quadrature formula and new inequalities for the generalized arithmetic and p-Logarithmic means are derived. This paper’s findings represent a significant improvement over previously published results. The paper’s ideas and formidable tools may inspire and motivate further research in this worthy and fascinating field. |
| first_indexed | 2024-09-25T03:41:33Z |
| format | Article |
| id | upm.eprints-109195 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-09-25T03:41:33Z |
| publishDate | 2023 |
| publisher | Multidisciplinary Digital Publishing Institute |
| record_format | dspace |
| spelling | upm.eprints-1091952024-08-27T04:48:33Z http://psasir.upm.edu.my/id/eprint/109195/ Some new fractal Milne-type integral inequalities via generalized convexity with applications Meftah, Badreddine Lakhdari, Abdelghani Saleh, Wedad Kilicman, Adem This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set. To that end, we develop a novel generalized integral identity involving first-order generalized derivatives. Finally, as applications, some error estimates for the Milne-type quadrature formula and new inequalities for the generalized arithmetic and p-Logarithmic means are derived. This paper’s findings represent a significant improvement over previously published results. The paper’s ideas and formidable tools may inspire and motivate further research in this worthy and fascinating field. Multidisciplinary Digital Publishing Institute 2023-02-07 Article PeerReviewed Meftah, Badreddine and Lakhdari, Abdelghani and Saleh, Wedad and Kilicman, Adem (2023) Some new fractal Milne-type integral inequalities via generalized convexity with applications. Fractal and Fractional, 7 (2). art. no. 166. pp. 1-15. ISSN 2504-3110 https://www.mdpi.com/2504-3110/7/2/166 10.3390/fractalfract7020166 |
| spellingShingle | Meftah, Badreddine Lakhdari, Abdelghani Saleh, Wedad Kilicman, Adem Some new fractal Milne-type integral inequalities via generalized convexity with applications |
| title | Some new fractal Milne-type integral inequalities via generalized convexity with applications |
| title_full | Some new fractal Milne-type integral inequalities via generalized convexity with applications |
| title_fullStr | Some new fractal Milne-type integral inequalities via generalized convexity with applications |
| title_full_unstemmed | Some new fractal Milne-type integral inequalities via generalized convexity with applications |
| title_short | Some new fractal Milne-type integral inequalities via generalized convexity with applications |
| title_sort | some new fractal milne type integral inequalities via generalized convexity with applications |
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