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We also consider the case of homogeneous kernel as well as certain operator expressions.<\/jats:p>","DOI":"10.3390\/axioms12070677","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T01:58:14Z","timestamp":1689040694000},"page":"677","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Equivalent Form Related to a Hilbert-Type Integral Inequality"],"prefix":"10.3390","volume":"12","author":[{"given":"Michael Th.","family":"Rassias","sequence":"first","affiliation":[{"name":"Department of Mathematics and Engineering Sciences, Hellenic Military Academy, 16673 Vari Attikis, Greece"},{"name":"Program in Interdisciplinary Studies, Institute for Advanced Study, 1 Einstein Dr, Princeton, NJ 08540, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bicheng","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrei","family":"Raigorodskii","sequence":"additional","affiliation":[{"name":"Moscow Institute of Physics and Technology, Institutskiy per, d. 9, 141700 Dolgoprudny, Russia"},{"name":"Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia"},{"name":"Caucasus Mathematical Center, Adyghe State University, 385000 Maykop, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,10]]},"reference":[{"key":"ref_1","first-page":"45","article-title":"Note on a theorem of Hilbert concerning series of positive terms","volume":"23","author":"Hardy","year":"1925","journal-title":"Proc. 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