Hybrid Integral Inequalities on Fractal Set
AXIOMS, sa.5, 2025 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2025
- Doi Numarası: 10.3390/axioms14050358
- Dergi Adı: AXIOMS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
- Kocaeli Üniversitesi Adresli: Evet
Özet
In this study, we introduce a new hybrid identity that effectively combines Newton-Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson's second rule and the left- and right-Radau two-point rules, among others. Building upon this flexible framework, we establish several new biparametrized fractal integral inequalities for functions whose local fractional derivatives are of a generalized convex type. In addition to employing tools from local fractional calculus, our approach utilizes the H & ouml;lder inequality, the power mean inequality, and a refined version of the latter. Further results are also derived using the concept of generalized concavity. To support our theoretical findings, we provide a graphical example that illustrates the validity of the obtained results, along with some practical applications that demonstrate their effectiveness.