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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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-03-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03281-y |
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| author | Jiao Yu Lin Han |
| author_facet | Jiao Yu Lin Han |
| author_sort | Jiao Yu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8b12acf8e3fd40b79a43cb1745d2afb0 |
| institution | DOAJ |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-8b12acf8e3fd40b79a43cb1745d2afb02025-08-20T03:01:55ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-03-012025111410.1186/s13660-025-03281-ySome Carleman-type inequalities in ( p , q ) $(p,q)$ -calculusJiao Yu0Lin Han1Institute of Public Foundation, Ningbo PolytechnicInstitute of Public Foundation, Ningbo PolytechnicAbstract 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.https://doi.org/10.1186/s13660-025-03281-y( p , q ) $(p,q)$ -Differential( p , q ) $(p,q)$ -Integration( p , q ) $(p,q)$ -Carleman inequality( p , q ) $(p,q)$ -Jessen inequality |
| spellingShingle | Jiao Yu Lin Han Some Carleman-type inequalities in ( p , q ) $(p,q)$ -calculus Journal of Inequalities and Applications ( p , q ) $(p,q)$ -Differential ( p , q ) $(p,q)$ -Integration ( p , q ) $(p,q)$ -Carleman inequality ( p , q ) $(p,q)$ -Jessen inequality |
| title | Some Carleman-type inequalities in ( p , q ) $(p,q)$ -calculus |
| title_full | Some Carleman-type inequalities in ( p , q ) $(p,q)$ -calculus |
| title_fullStr | Some Carleman-type inequalities in ( p , q ) $(p,q)$ -calculus |
| title_full_unstemmed | Some Carleman-type inequalities in ( p , q ) $(p,q)$ -calculus |
| title_short | Some Carleman-type inequalities in ( p , q ) $(p,q)$ -calculus |
| title_sort | some carleman type inequalities in p q p q calculus |
| topic | ( p , q ) $(p,q)$ -Differential ( p , q ) $(p,q)$ -Integration ( p , q ) $(p,q)$ -Carleman inequality ( p , q ) $(p,q)$ -Jessen inequality |
| url | https://doi.org/10.1186/s13660-025-03281-y |
| work_keys_str_mv | AT jiaoyu somecarlemantypeinequalitiesinpqpqcalculus AT linhan somecarlemantypeinequalitiesinpqpqcalculus |