{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:53:56Z","timestamp":1760151236180,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,5]],"date-time":"2022-03-05T00:00:00Z","timestamp":1646438400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In our 2014 work with M. Gabour, we introduced a metric space of generalized nonexpansive self-mappings of bounded and closed subsets of a Banach space and studied, using the Baire category approach, the asymptotic behavior of iterates of a generic operator belonging to this class. In the definition of a generalized nonexpansive mapping the norm is replaced by a general function which can be symmetric as a particular case. In this paper, we prove the convergence of infinite products of generalized nonexpansive self-mappings to a common fixed point in a generic setting.<\/jats:p>","DOI":"10.3390\/sym14030534","type":"journal-article","created":{"date-parts":[[2022,3,6]],"date-time":"2022-03-06T20:40:02Z","timestamp":1646599202000},"page":"534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Two Generic Convergence Results for Infinite Products of Generalized Nonexpansive Mappings"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0780-1559","authenticated-orcid":false,"given":"Simeon","family":"Reich","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander J.","family":"Zaslavski","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,5]]},"reference":[{"key":"ref_1","first-page":"343","article-title":"Fixed points for nonexpansive mappings and generalized nonexpansive mappings on Banach lattices","volume":"1","author":"Benavides","year":"2016","journal-title":"Pure Appl. 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Springer Optimization and Its Applications, Springer.","DOI":"10.1007\/978-3-319-33255-0"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zaslavski, A.J. (2018). Algorithms for solving common fixed point problems. Springer Optimization and Its Applications, Springer.","DOI":"10.1007\/978-3-319-77437-4"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leur application aux \u00e9quations int\u00e9grales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. Math."},{"key":"ref_12","first-page":"565","article-title":"Algorithms and convergence results of projection methods for inconsistent feasibility problems: A review","volume":"3","author":"Censor","year":"2018","journal-title":"Pure Appl. Func. 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On a class of generalized nonexpansive mappings. Mathematics, 8.","DOI":"10.3390\/math8071085"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/3\/534\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:32:31Z","timestamp":1760135551000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/3\/534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,5]]},"references-count":21,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["sym14030534"],"URL":"https:\/\/doi.org\/10.3390\/sym14030534","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,3,5]]}}}