The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator

Fallah Andevari, Hadiseh; Babakhani, Azizollah; Oliveira, Daniela D. Santos

doi:10.22130/scma.2023.2005455.1364

Articles in Press

Document Type : Research Paper

Authors

¹ Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol 47148-71167, Iran.

² Institute of Science and Technology, Federal University of S˜ao Paulo, S˜ao Jos´e dos Campos-SP, 12247-014, Brazil.

https://doi.org/10.22130/scma.2023.2005455.1364

Abstract

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.

Keywords

Main Subjects

Pseudo-Integrals

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Sahand Communications in Mathematical Analysis

The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator

References

References

Articles in Press, Accepted Manuscript
Available Online from 19 February 2024

The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator

References

References

Articles in Press, Accepted Manuscript Available Online from 19 February 2024

Articles in Press, Accepted Manuscript
Available Online from 19 February 2024