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Article

An Equivalent Form Related to a Hilbert-Type Integral Inequality

by
Michael Th. Rassias
1,2,*,
Bicheng Yang
3 and
Andrei Raigorodskii
4,5,6
1
Department of Mathematics and Engineering Sciences, Hellenic Military Academy, 16673 Vari Attikis, Greece
2
Program in Interdisciplinary Studies, Institute for Advanced Study, 1 Einstein Dr, Princeton, NJ 08540, USA
3
Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
4
Moscow Institute of Physics and Technology, Institutskiy per, d. 9, 141700 Dolgoprudny, Russia
5
Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia
6
Caucasus Mathematical Center, Adyghe State University, 385000 Maykop, Russia
*
Author to whom correspondence should be addressed.
Axioms 2023, 12(7), 677; https://doi.org/10.3390/axioms12070677
Submission received: 31 May 2023 / Revised: 24 June 2023 / Accepted: 6 July 2023 / Published: 10 July 2023
(This article belongs to the Special Issue Differential Equations and Dynamical Systems—Theory and Applications)
Versions Notes

Abstract

In the present paper, we establish an equivalent form related to a Hilbert-type integral inequality with a non-homogeneous kernel and a best possible constant factor. We also consider the case of homogeneous kernel as well as certain operator expressions.
Keywords: Hilbert-type integral inequality; weight function; equivalent form; operator; norm Hilbert-type integral inequality; weight function; equivalent form; operator; norm

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MDPI and ACS Style

Rassias, M.T.; Yang, B.; Raigorodskii, A. An Equivalent Form Related to a Hilbert-Type Integral Inequality. Axioms 2023, 12, 677. https://doi.org/10.3390/axioms12070677

AMA Style

Rassias MT, Yang B, Raigorodskii A. An Equivalent Form Related to a Hilbert-Type Integral Inequality. Axioms. 2023; 12(7):677. https://doi.org/10.3390/axioms12070677

Chicago/Turabian Style

Rassias, Michael Th., Bicheng Yang, and Andrei Raigorodskii. 2023. "An Equivalent Form Related to a Hilbert-Type Integral Inequality" Axioms 12, no. 7: 677. https://doi.org/10.3390/axioms12070677

APA Style

Rassias, M. T., Yang, B., & Raigorodskii, A. (2023). An Equivalent Form Related to a Hilbert-Type Integral Inequality. Axioms, 12(7), 677. https://doi.org/10.3390/axioms12070677

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