On Some Generalized Simpson’s and Newton’s Inequalities for (α, m)-Convex Functions in q-Calculus
Abstract
:1. Introduction
2. Preliminaries of q-Calculus and Some Inequalities
- (i)
- The product is q-differentiable on with
- (ii)
- If , then is q-differentiable on with
- (i)
- ;
- (ii)
- for .
3. Identities
4. Simpson’s Formula Type Inequalities
5. Simpson’s Formula Type Inequalities
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Sial, I.B.; Mei, S.; Ali, M.A.; Nonlaopon, K. On Some Generalized Simpson’s and Newton’s Inequalities for (α, m)-Convex Functions in q-Calculus. Mathematics 2021, 9, 3266. https://doi.org/10.3390/math9243266
Sial IB, Mei S, Ali MA, Nonlaopon K. On Some Generalized Simpson’s and Newton’s Inequalities for (α, m)-Convex Functions in q-Calculus. Mathematics. 2021; 9(24):3266. https://doi.org/10.3390/math9243266
Chicago/Turabian StyleSial, Ifra Bashir, Sun Mei, Muhammad Aamir Ali, and Kamsing Nonlaopon. 2021. "On Some Generalized Simpson’s and Newton’s Inequalities for (α, m)-Convex Functions in q-Calculus" Mathematics 9, no. 24: 3266. https://doi.org/10.3390/math9243266
APA StyleSial, I. B., Mei, S., Ali, M. A., & Nonlaopon, K. (2021). On Some Generalized Simpson’s and Newton’s Inequalities for (α, m)-Convex Functions in q-Calculus. Mathematics, 9(24), 3266. https://doi.org/10.3390/math9243266