Pub Date : 2010-05-01DOI: 10.1088/0266-5611/26/5/055007
Yair Censor, Alexander Segal
We propose the split common fixed point problem that requires to find a common fixed point of a family of operators in one space whose image under a linear transformation is a common fixed point of another family of operators in the image space. We formulate and analyze a parallel algorithm for solving this split common fixed point problem for the class of directed operators and note how it unifies and generalizes previously discussed problems and algorithms.
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V. Colao, Laurentiu Leustean, G. López, Victoria Martín-Márquez
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.
{"title":"Alternative iterative methods for nonexpansive mappings, rates of convergence and applications","authors":"V. Colao, Laurentiu Leustean, G. López, Victoria Martín-Márquez","doi":"10.14760/OWP-2009-19","DOIUrl":"https://doi.org/10.14760/OWP-2009-19","url":null,"abstract":"Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.","PeriodicalId":54853,"journal":{"name":"Journal of Convex Analysis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2009-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66621911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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