Abstract
In this work, we introduce generalized Raina fractional integral operators and derive Chebyshev-type inequalities involving these operators. In a first stage, we obtain Chebyshev-type inequalities for one product of functions. Then we extend those results to account for arbitrary products. Also, we establish some inequalities of the Chebyshev type for functions whose derivatives are bounded. In addition, we derive an estimate for the Chebyshev functional by applying the generalized Raina fractional integral operators. As corollaries of this study, some known results are recaptured from our general Chebyshev inequalities. The results of this work may prove useful in the theoretical analysis of numerical models to solve generalized Raina-type fractional-order integro-differential equations.
| Original language | English |
|---|---|
| Pages (from-to) | 10256-10275 |
| Number of pages | 20 |
| Journal | AIMS Mathematics |
| Volume | 7 |
| Issue number | 6 |
| DOIs | |
| State | Published - 22 Mar 2022 |
Bibliographical note
Publisher Copyright:© 2022 the Author(s), licensee AIMS Press.
Funding
This work was supported by the Taif University Researchers Supporting Project (No. TURSP-2020/155), Taif University, Taif, Saudi Arabia. The corresponding author (J. E. Macias-Diaz) was funded by the National Council for Science and Technology of Mexico (CONACYT) through grant A1-S-45928.
| Funders | Funder number |
|---|---|
| Consejo Nacional de Ciencia y Tecnología | A1-S-45928 |
| Taif University | TURSP-2020/155 |
Keywords
- Approximation techniques
- Chebyshev inequality
- Fractional-order integrals
- Generalized Raina integral operators
- Integral inequalities