An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces

In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid des...

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Bibliographic Details
Published inOptimization Vol. 68; no. 1; pp. 13 - 32
Main Authors Gibali, Aviv, Shehu, Yekini
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.01.2019
Taylor & Francis LLC
Subjects
Fixed points
Fixed points (mathematics)
Hilbert space
Iterative methods
Mapping
Projection and contraction method
Strong convergence
Subgradient extragradient method
Variational inequalities
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Summary:In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid descent approximation method, a new and efficient iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established under standard and mild conditions. Our scheme generalizes and extends some of the existing results in the literature, and moreover, its computational effort is less per each iteration compared with related works.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2018.1490417