{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T11:44:57Z","timestamp":1772883897149,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,21]],"date-time":"2023-01-21T00:00:00Z","timestamp":1674259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Distinguished Scientist Fellowship Program at King Saud University, Riyadh, Saudi Arabia","award":["RSP2023R187"],"award-info":[{"award-number":["RSP2023R187"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The aim of this paper is to provide new upper bounds of \u03c9(T), which denotes the numerical radius of a bounded operator T on a Hilbert space (H,\u27e8\u00b7,\u00b7\u27e9). We show the Acz\u00e9l inequality in terms of the operator |T|. Next, we give certain inequalities about the A-numerical radius \u03c9A(T) and the A-operator seminorm \u2225T\u2225A of an operator T. We also present several results related to the A-numerical radius of 2\u00d72 block matrices of semi-Hilbert space operators, by using symmetric 2\u00d72 block matrices.<\/jats:p>","DOI":"10.3390\/sym15020304","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T03:26:41Z","timestamp":1674444401000},"page":"304","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["On Some Generalizations of Cauchy\u2013Schwarz Inequalities and Their Applications"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7442-8841","authenticated-orcid":false,"given":"Najla","family":"Altwaijry","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9326-4173","authenticated-orcid":false,"given":"Kais","family":"Feki","sequence":"additional","affiliation":[{"name":"Faculty of Economic Sciences and Management of Mahdia, University of Monastir, Mahdia 5111, Tunisia"},{"name":"Laboratory Physics-Mathematics and Applications (LR\/13\/ES-22), Faculty of Sciences of Sfax, University of Sfax, Sfax 3018, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0716-293X","authenticated-orcid":false,"given":"Nicu\u015for","family":"Minculete","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Transilvania University of Brasov, 500091 Brasov, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,21]]},"reference":[{"key":"ref_1","unstructured":"Furuta, T. 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