{"title":"The Split Common Fixed Point Problem for Directed Operators.","authors":"Yair Censor, Alexander Segal","doi":"10.1088/0266-5611/26/5/055007","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":54853,"journal":{"name":"Journal of Convex Analysis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2010-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/0266-5611/26/5/055007","citationCount":"401","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Convex Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/0266-5611/26/5/055007","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 401
Abstract
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.
期刊介绍：
The concern of this international mathematical journal is to disseminate theoretical
knowledge in the field of Convex Analysis and, at the same time, cultivate and
extend its applications. In this sense it publishes research articles touching the areas
of Calculus of Variations, Control Theory, Measure Theory, Functional Analysis,
Differential Equations, Integral Equations, Optimization and Mathematical Programming,
and Mathematical Economics. Of particular interest are topics related to nonsmooth analysis,
generalized differentiability, and set-valued functions.
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