{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:51:52Z","timestamp":1760143912501,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T00:00:00Z","timestamp":1709683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University","award":["RSP2024R187"],"award-info":[{"award-number":["RSP2024R187"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Consider the power series with complex coefficients h(z)=\u2211k=0\u221eakzk and its modified version ha(z)=\u2211k=0\u221e|ak|zk. In this article, we explore the application of certain H\u00f6lder-type inequalities for deriving various inequalities for operators acting on the aforementioned power series. We establish these inequalities under the assumption of the convergence of h(z) on the open disk D(0,\u03c1), where \u03c1 denotes the radius of convergence. Additionally, we investigate the norm and numerical radius inequalities associated with these concepts.<\/jats:p>","DOI":"10.3390\/axioms13030172","type":"journal-article","created":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T04:19:02Z","timestamp":1709785142000},"page":"172","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["H\u00f6lder-Type Inequalities for Power Series of Operators in Hilbert Spaces"],"prefix":"10.3390","volume":"13","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\/0000-0003-2902-6805","authenticated-orcid":false,"given":"Silvestru Sever","family":"Dragomir","sequence":"additional","affiliation":[{"name":"Applied Mathematics Research Group, ISILC, 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":[[2024,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"97","DOI":"10.4064\/sm227-2-1","article-title":"Notes on some spectral radius and numerical radius inequalities","volume":"227","author":"Kittaneh","year":"2015","journal-title":"Stud. 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