1. Some New Fractal Milne-Type Integral Inequalities via Generalized Convexity with Applications.
- Author
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Meftah, Badreddine, Lakhdari, Abdelghani, Saleh, Wedad, and Kiliçman, Adem
- Subjects
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INTEGRAL inequalities , *FRACTALS , *GENERALIZED integrals , *INTEGRAL functions , *CONVEX sets , *ARITHMETIC - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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