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

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대한수학회 (The Korean Mathematical Society)|2021.05|대한수학회지 (Journal of the KMS)|제58권 제3호|pp. 525-552|DOI 10.4134/JKMS.j180808

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키워드

fixed pointsvariational inequalityzerosMaximal monotone operatorcontinuous monotone mappingcontinuous pseudocontractive mappingminimum-norm point
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초록

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.

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.

참고문헌 (20)

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