General iterative algorithms for monotone inclusion, variational inequality and fixed point problems

Pub Date : 2021-05-01 DOI:10.4134/JKMS.J180808
J. Jung
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Abstract

In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.
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单调包含、变分不等式和不动点问题的一般迭代算法
本文介绍了两种寻找连续单调映射变分不等式问题解集公共元素的一般迭代算法(一种隐式算法和一种显式算法),集值极大单调算子的零点集和Hilbert空间中连续伪压缩映射的不动点集。然后,我们建立了所提出的迭代算法到三个集合的公共点的强收敛性,这是一个变分不等式的解。进一步,我们在三个集合的公共集合中找到了最小范数元素。
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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