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Regularization Methods for Nonexpansive Semigroups in Hilbert Spaces

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Abstract

The purpose of this paper is to present a regularization method for finding a common fixed point of a nonexpansive semigroup in a real Hilbert space. A combination of the considered regularization scheme with the proximal point algorithm and another one of the regularization method with an iterative scheme is studied in this research. We also discuss an application of the proposed methods for an initial value problem in Hilbert spaces.

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Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED). We are very grateful to the referees for their really helpful and constructive comments.

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Authors and Affiliations

  1. University of Agriculture and Forestry, Thai Nguyen University, Thai Nguyen, Vietnam

    Pham Thanh Hieu

  2. University of Sciences, Thai Nguyen University, Thai Nguyen, Vietnam

    Nguyen Thi Thu Thuy

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  1. Pham Thanh Hieu
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  2. Nguyen Thi Thu Thuy
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Correspondence to Nguyen Thi Thu Thuy.

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Hieu, P.T., Thu Thuy, N.T. Regularization Methods for Nonexpansive Semigroups in Hilbert Spaces. Vietnam J. Math. 44, 637–648 (2016). https://doi.org/10.1007/s10013-015-0178-3

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  • DOI: https://doi.org/10.1007/s10013-015-0178-3

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