The Split Common Fixed Point Problem for Directed Operators.

IF 0.6 4区数学 Q3 MATHEMATICS

Journal of Convex Analysis Pub Date : 2010-05-01 DOI:10.1088/0266-5611/26/5/055007

Yair Censor, Alexander Segal

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.

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有向算子的分裂公共不动点问题。

我们提出了分离公共不动点问题，要求在一个空间中找到一个算子族的公共不动点，该算子族在线性变换下的像是另一个算子族在像空间中的公共不动点。我们制定并分析了一个并行算法来解决这类有向算子的分裂公共不动点问题，并注意到它是如何统一和推广前面讨论的问题和算法的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Convex Analysis 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

6-12 weeks

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.