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Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces

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Abstract

Building upon the subgradient extragradient method proposed by Censor et al., we prove the strong convergence of the iterative sequence generated by a modification of this method by means of the Halpern method. We also consider the problem of finding a common element of the solution set of a variational inequality and the fixed-point set of a quasi-nonexpansive mapping with a demiclosedness property.

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Acknowledgements

The authors thank Professor Franco Giannessi and the two referees for their insightful suggestions. The second author is supported by the TRF Research Career Development Grant (RSA5680002).

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  1. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

    Rapeepan Kraikaew & Satit Saejung

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  1. Rapeepan Kraikaew
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  2. Satit Saejung
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Correspondence to Satit Saejung.

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Kraikaew, R., Saejung, S. Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces. J Optim Theory Appl 163, 399–412 (2014). https://doi.org/10.1007/s10957-013-0494-2

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  • DOI: https://doi.org/10.1007/s10957-013-0494-2

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