New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals
Abstract
:1. Introduction
2. New Generalized Fractional Integrals Identity and New Integral Inequality for Katugampola Fractional Integrals
3. Generalized Hermite-Hadamard Inequality and Related Integral Inequalities for Katugampola Fractional Integral on Fractal Sets
- 1.
- If and , we have the trapezoid inequality:
- 2.
- For , we have
- 1.
- For , we get
- 2.
- If , we have
4. Applications to Special Means
- The arithmetic mean:; , with .
- The generalized log-mean:; , with .
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Almutairi, O.; Kılıçman, A. New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals. Symmetry 2020, 12, 568. https://doi.org/10.3390/sym12040568
Almutairi O, Kılıçman A. New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals. Symmetry. 2020; 12(4):568. https://doi.org/10.3390/sym12040568
Chicago/Turabian StyleAlmutairi, Ohud, and Adem Kılıçman. 2020. "New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals" Symmetry 12, no. 4: 568. https://doi.org/10.3390/sym12040568