{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:37:37Z","timestamp":1787341057811,"version":"build-2736575974"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["389\/12"],"award-info":[{"award-number":["389\/12"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"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\/501100006260","name":"Technion-Israel Institute of Technology","doi-asserted-by":"publisher","award":["N00014-12-1-0997"],"award-info":[{"award-number":["N00014-12-1-0997"]}],"id":[{"id":"10.13039\/501100006260","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly, and linearly regular sequences of operators. We show that the type of the regularity is preserved under relaxations, convex combinations, and products of operators. Moreover, in this connection, we show that weak, bounded, and linear regularity lead to weak, strong, and linear convergence, respectively, of various iterative methods. This applies, in particular, to block iterative and string averaging projection methods, which, in principle, are based on the abovementioned algebraic operations applied to projections. Finally, we show an application of regular sequences of operators to variational inequality problems.<\/jats:p>","DOI":"10.1137\/17m1134986","type":"journal-article","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T11:53:02Z","timestamp":1525780382000},"page":"1508-1532","source":"Crossref","is-referenced-by-count":39,"title":["Regular Sequences of Quasi-Nonexpansive Operators and Their Applications"],"prefix":"10.1137","volume":"28","author":[{"given":"Andrzej","family":"Cegielski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simeon","family":"Reich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rafa\u0142","family":"Zalas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,5,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(89)90375-3"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.01.087"},{"key":"atypb3","first-page":"67","volume":"3","author":"Aoyama K.","year":"2012","journal-title":"J. Nonlinear Anal. Optim."},{"key":"atypb4","first-page":"10","volume":"17","author":"Aoyama K.","year":"2014","journal-title":"Fixed Point Theory Appl."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1996.0308"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144593251710"},{"key":"atypb7","first-page":"129","volume":"15","author":"Bauschke H.H.","year":"2014","journal-title":"J. Nonlinear Convex Anal."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.06.075"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/14096267X"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-017-0310-4"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/15M1045223"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1966-11544-6"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"A. Cegielski,\n                      Iterative Methods for Fixed Point Problems in Hilbert Spaces\n                      , Lecture Notes in Math. 2057, Springer, Heidelberg, 2012.","DOI":"10.1007\/978-3-642-30901-4"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/15M1012438"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-014-0662-z"},{"key":"atypb16","first-page":"139","author":"Cegielski A.","year":"2016","journal-title":"PA"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2016.1147038"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2012.716807"},{"key":"atypb19","first-page":"399","volume":"15","author":"Cegielski A.","year":"2014","journal-title":"Fixed Point Theory"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/S1076-5670(08)70157-5"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02683333"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02017349"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(84)90051-7"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s11784-015-0256-x"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2016.1271800"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.12.064"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2003.11.004"},{"key":"atypb28","unstructured":"U. Kohlenbach, G. Lo\u0301pez-Acedo, and A. Nicolae,\n                      Moduli of Regularity and Rates of Convergence for Feje\u0301r Monotone Sequences\n                      , preprint, arXiv:1711.02130v1, 2017."},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1137\/16M1087333"},{"key":"atypb30","first-page":"411","volume":"4","author":"Matous\u030ckova\u0301 E.","year":"2003","journal-title":"J. Nonlinear Convex Anal."},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11761-0"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1969.30.747"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(73)90087-5"},{"key":"atypb34","first-page":"331","volume":"18","author":"Reich S.","year":"2017","journal-title":"J. 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