Some Carleman-type inequalities in ( p , q ) $(p,q)$ -calculus
Abstract In this paper, we construct ( p , q ) $\left (p,q\right )$ -type Jessen’s inequality using the properties of convex functions. On this basis, we generalize the classical Carleman integral-type inequality in ( p , q ) $\left (p,q\right )$ -calculus and obtain various forms of ( p , q ) $\lef...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03281-y |
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| Summary: | Abstract In this paper, we construct ( p , q ) $\left (p,q\right )$ -type Jessen’s inequality using the properties of convex functions. On this basis, we generalize the classical Carleman integral-type inequality in ( p , q ) $\left (p,q\right )$ -calculus and obtain various forms of ( p , q ) $\left (p,q\right )$ -integral-type Carleman’s inequality by introducing various types of weight functions. Furthermore, we verify that under specific conditions, the ( p , q ) $\left (p,q\right )$ -integral Carleman inequality can reduce to the classical Carleman inequality in calculus. |
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| ISSN: | 1029-242X |