A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions
Abstract
:1. Introduction
- If , and , then the generalized fractional integral operators reduce to the classical R.L integrals.
- If , and , then Definition 3 reduces to Definition 1.
2. Inequalities of the Hermite–Hadamard–Mercer Type for Convex Functions
3. Inequalities of the Hermite–Hadamard–Mercer Type for Fractional Integrals
4. Inequalities of the Hermite–Hadamard–Mercer Type for Generalized Fractional Integral Operators
5. Applications: Special Means
- (1)
- The arithmetic mean:
- (2)
- The generalized logarithmic mean:
6. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Hussain, T.; Ciurdariu, L.; Grecu, E. A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions. Mathematics 2024, 12, 3711. https://doi.org/10.3390/math12233711
Hussain T, Ciurdariu L, Grecu E. A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions. Mathematics. 2024; 12(23):3711. https://doi.org/10.3390/math12233711
Chicago/Turabian StyleHussain, Talib, Loredana Ciurdariu, and Eugenia Grecu. 2024. "A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions" Mathematics 12, no. 23: 3711. https://doi.org/10.3390/math12233711
APA StyleHussain, T., Ciurdariu, L., & Grecu, E. (2024). A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions. Mathematics, 12(23), 3711. https://doi.org/10.3390/math12233711