A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions
The goal of this study is to develop numerous Hermite–Hadamard–Mercer (H–H–M)-type inequalities involving various fractional integral operators, including classical, Riemann–Liouville (R.L), k-Riemann–Liouville (k-R.L), and their generalized fractional integral operators. In addition, we establish a...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/23/3711 |
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| Summary: | The goal of this study is to develop numerous Hermite–Hadamard–Mercer (H–H–M)-type inequalities involving various fractional integral operators, including classical, Riemann–Liouville (R.L), k-Riemann–Liouville (k-R.L), and their generalized fractional integral operators. In addition, we establish a number of corresponding fractional integral inequalities for three-times differentiable convex functions that are connected to the right side of the H–H–M-type inequality. For these results, further remarks and observations are provided. Following that, a couple of graphical representations are shown to highlight the key findings of our study. Finally, some applications on special means are shown to demonstrate the effectiveness of our inequalities. |
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| ISSN: | 2227-7390 |