{"title":"关于具有凸和紧点映象的映射的逐次逼近的一般收敛性。","authors":"Christian Bargetz, Emir Medjic, Katriin Pirk","doi":"10.1007/s00605-022-01813-y","DOIUrl":null,"url":null,"abstract":"<p><p>We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping and typical points of its domain the sequence of successive approximations is unique and converges to a fixed point of the mapping.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10576736/pdf/","citationCount":"0","resultStr":"{\"title\":\"On generic convergence of successive approximations of mappings with convex and compact point images.\",\"authors\":\"Christian Bargetz, Emir Medjic, Katriin Pirk\",\"doi\":\"10.1007/s00605-022-01813-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping and typical points of its domain the sequence of successive approximations is unique and converges to a fixed point of the mapping.</p>\",\"PeriodicalId\":54737,\"journal\":{\"name\":\"Monatshefte fur Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10576736/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Monatshefte fur Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00605-022-01813-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2022/12/22 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte fur Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00605-022-01813-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/12/22 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On generic convergence of successive approximations of mappings with convex and compact point images.
We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping and typical points of its domain the sequence of successive approximations is unique and converges to a fixed point of the mapping.
期刊介绍：
The journal was founded in 1890 by G. v. Escherich and E. Weyr as "Monatshefte für Mathematik und Physik" and appeared with this title until 1944. Continued from 1948 on as "Monatshefte für Mathematik", its managing editors were L. Gegenbauer, F. Mertens, W. Wirtinger, H. Hahn, Ph. Furtwängler, J. Radon, K. Mayrhofer, N. Hofreiter, H. Reiter, K. Sigmund, J. Cigler.
The journal is devoted to research in mathematics in its broadest sense. Over the years, it has attracted a remarkable cast of authors, ranging from G. Peano, and A. Tauber to P. Erdös and B. L. van der Waerden. The volumes of the Monatshefte contain historical achievements in analysis (L. Bieberbach, H. Hahn, E. Helly, R. Nevanlinna, J. Radon, F. Riesz, W. Wirtinger), topology (K. Menger, K. Kuratowski, L. Vietoris, K. Reidemeister), and number theory (F. Mertens, Ph. Furtwängler, E. Hlawka, E. Landau). It also published landmark contributions by physicists such as M. Planck and W. Heisenberg and by philosophers such as R. Carnap and F. Waismann. In particular, the journal played a seminal role in analyzing the foundations of mathematics (L. E. J. Brouwer, A. Tarski and K. Gödel).
The journal publishes research papers of general interest in all areas of mathematics. Surveys of significant developments in the fields of pure and applied mathematics and mathematical physics may be occasionally included.
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