{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T14:31:54Z","timestamp":1775745114930,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T00:00:00Z","timestamp":1684108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["820\/17"],"award-info":[{"award-number":["820\/17"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["2001893"],"award-info":[{"award-number":["2001893"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["2016723"],"award-info":[{"award-number":["2016723"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fund for the Promotion of Research at the Technion","award":["820\/17"],"award-info":[{"award-number":["820\/17"]}]},{"name":"Fund for the Promotion of Research at the Technion","award":["2001893"],"award-info":[{"award-number":["2001893"]}]},{"name":"Fund for the Promotion of Research at the Technion","award":["2016723"],"award-info":[{"award-number":["2016723"]}]},{"name":"Technion General Research Fund","award":["820\/17"],"award-info":[{"award-number":["820\/17"]}]},{"name":"Technion General Research Fund","award":["2001893"],"award-info":[{"award-number":["2001893"]}]},{"name":"Technion General Research Fund","award":["2016723"],"award-info":[{"award-number":["2016723"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In 2006, together with D. Butnariu, we showed that if all iterates of a nonexpansive self-mapping of a complete metric space converge, then all its inexact iterates with summable computational errors converge too. In a recent paper of ours, we have extended this result to uniformly locally nonexpansive self-mappings of a complete metric space. In the present paper, we establish analogous results for uniformly locally nonexpansive mappings which take a nonempty closed subset of a complete metric space into the space. In the particular case of a Banach space, if the operator is symmetric, then the set of all limit points of its iterates is also symmetric.<\/jats:p>","DOI":"10.3390\/sym15051084","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T08:28:56Z","timestamp":1684139336000},"page":"1084","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Three Convergence Results for Inexact Iterates of Uniformly Locally Nonexpansive Mappings"],"prefix":"10.3390","volume":"15","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":[[2023,5,15]]},"reference":[{"key":"ref_1","first-page":"343","article-title":"Fixed points for nonexpansive mappings and generalized nonexpansive mappings on Banach lattices","volume":"1","year":"2016","journal-title":"Pure Appl. Func. Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0362-546X(82)90083-9","article-title":"Strong and weak convergence theorems for locally nonexpansive mappings in Banach spaces","volume":"6","author":"Bruck","year":"1982","journal-title":"Nonlinear Anal."},{"key":"ref_3","unstructured":"Butnariu, D., Reich, S., and Zaslavski, A.J. (2006). Fixed Point Theory and Its Applications, Yokohama Publishers."},{"key":"ref_4","first-page":"185","article-title":"Sur la convergence des approximations successives pour les contractions non lin\u00e9aires dans un espace de Banach","volume":"283","author":"Myjak","year":"1976","journal-title":"C. R. Acad. Sci. Paris"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Goebel, K., and Kirk, W.A. (1990). Topics in Metric Fixed Point Theory, Cambridge University Press.","DOI":"10.1017\/CBO9780511526152"},{"key":"ref_6","unstructured":"Goebel, K., and Reich, S. (1984). Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker."},{"key":"ref_7","first-page":"657","article-title":"Extensions of the Dugundji-Granas and Nadler\u2019s theorems on the continuity of fixed points","volume":"2","author":"Jachymski","year":"2017","journal-title":"Pure Appl. Funct. Anal."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kirk, W.A. (2001). Handbook of Metric Fixed Point Theory, Kluwer.","DOI":"10.1007\/978-94-017-1748-9"},{"key":"ref_9","first-page":"63","article-title":"Extensions of Browder\u2019s demiclosedness principle and Reich\u2019s lemma and their applications","volume":"1","author":"Kubota","year":"2016","journal-title":"Pure Appl. Func. Anal."},{"key":"ref_10","first-page":"7","article-title":"An extension of Banach\u2019s contraction principle","volume":"12","author":"Edelstein","year":"1961","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1090\/S0002-9939-1962-0148046-1","article-title":"A note on contractive mappings","volume":"13","author":"Rakotch","year":"1962","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zaslavski, A.J. (2016). Approximate Solutions of Common Fixed Point Problems, Springer.","DOI":"10.1007\/978-3-319-33255-0"},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1109\/JSTSP.2007.910263","article-title":"Stable convergence behavior under summable perturbations of a class of projection methods for convex feasibility and optimization problems","volume":"1","author":"Butnariu","year":"2007","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1088\/0266-5611\/26\/6\/065008","article-title":"Perturbation resilience and superiorization of iterative algorithms","volume":"26","author":"Censor","year":"2010","journal-title":"Inverse Probl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1007\/s10957-013-0408-3","article-title":"Projected subgradient minimization versus superiorization","volume":"160","author":"Censor","year":"2014","journal-title":"J. Optim. Theory Appl."},{"key":"ref_17","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. Anal."},{"key":"ref_18","first-page":"243","article-title":"A new split inverse problem and an application to least intensity feasible solutions","volume":"2","author":"Gibali","year":"2017","journal-title":"Pure Appl. Funct. Anal."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"19p","DOI":"10.1088\/0266-5611\/28\/3\/035005","article-title":"Accelerated Perturbation-Resilient Block-Iterative Projection Methods with Application to Image Reconstruction","volume":"28","author":"Nikazad","year":"2012","journal-title":"Inverse Probl."},{"key":"ref_20","first-page":"685","article-title":"The split common fixed point problem and the shrinking projection method for new nonlinear mappings in two Banach spaces","volume":"2","author":"Takahashi","year":"2017","journal-title":"Pure Appl. Funct. Anal."},{"key":"ref_21","first-page":"349","article-title":"A general iterative method for split common fixed point problems in Hilbert spaces and applications","volume":"3","author":"Takahashi","year":"2018","journal-title":"Pure Appl. Funct. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1002\/zamm.19670470202","article-title":"The Round-Off Stability of Iterations","volume":"47","author":"Ostrowski","year":"1967","journal-title":"Z. Angew. Math. Mech."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.17654\/0973422822003","article-title":"Convergence of inexact iterates of uniformly locally nonexpansive mappings with summable errors","volume":"18","author":"Reich","year":"2022","journal-title":"JP J. Fixed Point Theory Appl."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Reich, S., and Zaslavski, A.J. (2014). Genericity in Nonlinear Analysis, Developments in Mathematics, Springer.","DOI":"10.1007\/978-1-4614-9533-8"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1084\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:35:00Z","timestamp":1760124900000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1084"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,15]]},"references-count":24,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["sym15051084"],"URL":"https:\/\/doi.org\/10.3390\/sym15051084","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,15]]}}}