New integral formulas with applications to integral inequalities
In this article, we derive new integral formulas involving a ratio function, a maximum function, and three adjustable parameters. Two of these parameters control the maximum function in di erent ways. The arctangent function plays a central role in the resulting expressions. These formulas are then...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2025-01-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/awutm-2025-0008 |
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| Summary: | In this article, we derive new integral formulas involving a ratio function, a maximum function, and three adjustable parameters. Two of these parameters control the maximum function in di erent ways. The arctangent function plays a central role in the resulting expressions. These formulas are then used to construct new and varied types of integral inequalities. In particular, we present weighted Hölder-type integral inequalities, as well as new Hardy-Hilbert-type integral inequalities. Their novelty lies mainly in the inclusion of the maximum function and the two parameters governing it. Detailed proofs are given. |
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| ISSN: | 1841-3307 |