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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University of Maragheh
2024-07-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_711323_956b3b56a176a212c0d6c51e416208a8.pdf |
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| author | Hadiseh Fallah Andevari Azizollah Babakhani Daniela Oliveira |
| author_facet | Hadiseh Fallah Andevari Azizollah Babakhani Daniela Oliveira |
| author_sort | Hadiseh Fallah Andevari |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5156cd5342054eefa15514a811a30180 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-5156cd5342054eefa15514a811a301802025-02-11T05:27:31ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-07-0121314716310.22130/scma.2023.2005455.1364711323The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-OperatorHadiseh Fallah Andevari0Azizollah Babakhani1Daniela Oliveira2Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol 47148-71167, Iran.Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol 47148-71167, Iran.Institute of Science and Technology, Federal University of S˜ao Paulo, S˜ao Jos´e dos Campos-SP, 12247-014, Brazil.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.https://scma.maragheh.ac.ir/article_711323_956b3b56a176a212c0d6c51e416208a8.pdfriemann-liouville fractional integralpseudo-analysissemiringh\"{o}lder's inequalityminkowski's inequality |
| spellingShingle | Hadiseh Fallah Andevari Azizollah Babakhani Daniela Oliveira The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator Sahand Communications in Mathematical Analysis riemann-liouville fractional integral pseudo-analysis semiring h\"{o}lder's inequality minkowski's inequality |
| title | The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator |
| title_full | The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator |
| title_fullStr | The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator |
| title_full_unstemmed | The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator |
| title_short | The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator |
| title_sort | holder and minkowski inequalities utilizing a fractional operator involvement of pseudo operator |
| topic | riemann-liouville fractional integral pseudo-analysis semiring h\"{o}lder's inequality minkowski's inequality |
| url | https://scma.maragheh.ac.ir/article_711323_956b3b56a176a212c0d6c51e416208a8.pdf |
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