{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T05:10:43Z","timestamp":1725340243936},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,16]],"date-time":"2023-04-16T00:00:00Z","timestamp":1681603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Prince sattam bin Abdulaziz University","award":["PSAU\/2023\/R\/1444"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"Hermite\u2013Hadamard inequalities and their refinements have been investigated for a long period of time. In this paper, we obtained refinements of the Hermite\u2013Hadamard inequality of tensorial type for the convex functions of self-adjoint operators in Hilbert spaces. The obtained inequalities generalize the previously obtained inequalities by Dragomir. We also provide useful Lemmas which enabled us to obtain the results. The examples of the obtained inequalities for specific convex functions have been given in the example and consequences section. Symmetry in the upper and lower bounds can be seen in the last Theorem of the paper given, as the upper and lower bounds differ by a constant.<\/jats:p>","DOI":"10.3390\/sym15040925","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T07:14:09Z","timestamp":1681715649000},"page":"925","source":"Crossref","is-referenced-by-count":4,"title":["Some Refinements of the Tensorial Inequalities in Hilbert Spaces"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-4244-4342","authenticated-orcid":false,"given":"Vuk","family":"Stojiljkovi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-9027-0810","authenticated-orcid":false,"given":"Rajagopalan","family":"Ramaswamy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz Univeristy, Al-Kharj 16278, Saudi Arabia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-1687-3212","authenticated-orcid":false,"given":"Ola A. Ashour","family":"Abdelnaby","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz Univeristy, Al-Kharj 16278, Saudi Arabia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-8254-6688","authenticated-orcid":false,"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mitrinovic, D.S. (1970). Analytic Inequalities, Springer.","DOI":"10.1007\/978-3-642-99970-3"},{"key":"ref_2","unstructured":"Pe\u010dari\u0107, J., Proschan, F., and Tong, Y. (1992). 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