Development of Fractional Newton-Type Inequalities Through Extended Integral Operators
Abstract
1. Introduction
- (i)
- Simpson’s one-third rule, often referred to as Simpson’s numerical integration method, is formulated as
- (ii)
- Simpson’s three-third rule, which extends the standard Simpson method, is a particular example of the Newton–Cotes family of numerical integration formulas:
2. An Identity
3. Newton-Type Inequalities for Convex Functions
4. Newton-Type Inequalities for Bounded Functions
5. Newton-Type Inequalities for Lipschitzian Functions
6. Newton-Type Inequalities for Functions of Bounded Variation
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
NTI | Newton-Type Inequality |
NTIs | Newton-Type Inequalities |
FR-L | Fractional Riemann–Liouville |
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Hyder, A.-A.; Almoneef, A.A.; Barakat, M.A.; Budak, H.; Aktaş, Ö. Development of Fractional Newton-Type Inequalities Through Extended Integral Operators. Fractal Fract. 2025, 9, 443. https://doi.org/10.3390/fractalfract9070443
Hyder A-A, Almoneef AA, Barakat MA, Budak H, Aktaş Ö. Development of Fractional Newton-Type Inequalities Through Extended Integral Operators. Fractal and Fractional. 2025; 9(7):443. https://doi.org/10.3390/fractalfract9070443
Chicago/Turabian StyleHyder, Abd-Allah, Areej A. Almoneef, Mohamed A. Barakat, Hüseyin Budak, and Özge Aktaş. 2025. "Development of Fractional Newton-Type Inequalities Through Extended Integral Operators" Fractal and Fractional 9, no. 7: 443. https://doi.org/10.3390/fractalfract9070443
APA StyleHyder, A.-A., Almoneef, A. A., Barakat, M. A., Budak, H., & Aktaş, Ö. (2025). Development of Fractional Newton-Type Inequalities Through Extended Integral Operators. Fractal and Fractional, 9(7), 443. https://doi.org/10.3390/fractalfract9070443