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A Two-Step Extragradient-Viscosity Method for Variational Inequalities and Fixed Point Problems

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Abstract

This paper develops a two-step extragradient-viscosity method for finding a common solution to a variational inequality problem and a fixed point problem in a Hilbert space. Combining the two-step extragradient algorithm and the viscosity one, we propose a strongly convergent method, which contains as special cases some existing algorithms. Several numerical experiments are implemented to demonstrate the performance of the proposed method in comparison with classical hybrid extragradient-like algorithms.

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Acknowledgements

The authors would like to thank the Associate Editor and anonymous referees for their valuable comments and suggestions which help us in improving the original version of this paper.

Funding

The first-named and last-named authors are supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the project: 101.01-2017.315.

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Authors and Affiliations

  1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Dang Van Hieu

  2. VNU, Hanoi University of Science, Hanoi, Vietnam

    Dang Xuan Son

  3. Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Pham Ky Anh

  4. TIMAS, Thang Long University, Hanoi, Vietnam

    Le Dung Muu

Authors
  1. Dang Van Hieu
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  2. Dang Xuan Son
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  3. Pham Ky Anh
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  4. Le Dung Muu
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Correspondence to Dang Van Hieu.

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Van Hieu, D., Son, D.X., Anh, P.K. et al. A Two-Step Extragradient-Viscosity Method for Variational Inequalities and Fixed Point Problems. Acta Math Vietnam 44, 531–552 (2019). https://doi.org/10.1007/s40306-018-0290-z

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  • DOI: https://doi.org/10.1007/s40306-018-0290-z

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