{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:36:34Z","timestamp":1760150194008,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T00:00:00Z","timestamp":1696291200000},"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","award":["RSP2023R187"],"award-info":[{"award-number":["RSP2023R187"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main focus of this paper is the study of the Selberg operator. It aims to establish appropriate bounds for the norm and numerical radius of the product of three bounded operators, with one of them being a Selberg operator. Moreover, it offers several bounds involving the summation of operators, notably the Selberg operator. Through the examination of these properties and relationships, this study contributes to a better understanding of the Selberg operator and its influence on operator compositions. The paper also highlights the significance of symmetry in mathematics and its potential implications across various mathematical domains.<\/jats:p>","DOI":"10.3390\/sym15101860","type":"journal-article","created":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T07:47:52Z","timestamp":1696405672000},"page":"1860","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Norm and Numerical Radius Inequalities Related to the Selberg Operator"],"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5699-4740","authenticated-orcid":false,"given":"Cristian","family":"Conde","sequence":"additional","affiliation":[{"name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas, Buenos Aires C1425FQB, Argentina"},{"name":"Instituto de Ciencias, Universidad Nacional de Gral. Sarmiento, J. M. Gutierrez 1150, Los Polvorines B1613GSX, Argentina"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2902-6805","authenticated-orcid":false,"given":"Silvestru Sever","family":"Dragomir","sequence":"additional","affiliation":[{"name":"Mathematics, College of Sport, Health and Engineering, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9326-4173","authenticated-orcid":false,"given":"Kais","family":"Feki","sequence":"additional","affiliation":[{"name":"Laboratory Physics-Mathematics and Applications (LR\/13\/ES-22), Faculty of Sciences of Sfax, University of Sfax, Sfax 3018, Tunisia"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gohberg, I.C., and Krein, M.G. (1969). Introduction to the Theory of Linear Nonselfadjoint Operators, American Mathematical Society.","DOI":"10.1090\/mmono\/018"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Aici, S., Frakis, A., and Kittaneh, F. (2023). Refinements of some numericalradius inequalities for operators. Rend. Circ. Mat. 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