The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator
A generalized integral operator of order $\alpha$ of a real function $f$ including a parameter set $P$, namely $K_P^\alpha f(t)$ has been introduced by O. P. Agrawal (Computers and Mathematics with Applications, 59 (2010) 1852--1864), which is a generalization of some important fractional integra...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2024-07-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_711323_956b3b56a176a212c0d6c51e416208a8.pdf |
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| Summary: | A generalized integral operator of order $\alpha$ of a real function $f$ including a parameter set $P$, namely $K_P^\alpha f(t)$ has been introduced by O. P. Agrawal (Computers and Mathematics with Applications, 59 (2010) 1852--1864), which is a generalization of some important fractional integrals such as the Riemann-Liouville fractional integral. Using pseudo-analysis, this paper introduces a pseudo-operator integral of order $\alpha$ including a parameter set $P$ in a semiring $([a, b], \oplus, \odot)$, which is a generalization of $K_P^\alpha f(t)$. We also discuss some particular cases and we obtain the well-known H\"{o}lder's and Minkowski's inequalities for this kind of pseudo-operator integral. The results given in this paper provide a generalization of several inequalities obtained in earlier studies. |
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| ISSN: | 2322-5807 2423-3900 |