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A new strong convergence for solving split variational inclusion problems

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Abstract

The purpose of this article is to propose an algorithm for finding an approximate solution of a split variational inclusion problem for monotone operators. By using inertial method, we get a new and simple algorithm for such a problem. Under standard assumptions, we study the strong convergence theorem of the proposed algorithm. As application, we study the split feasibility problem in real Hilbert spaces. Finally, for supporting the convergence of the proposed algorithm, we also consider several preliminary numerical experiments for solving signal recovery by compressed sensing.

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Acknowledgments

The authors would like to thank Professor Aviv Gibali and three anonymous reviewers for their comments on the manuscript which helped us very much in improving and presenting the original version of this paper. This work was partially supported by the National Foundation for Science and Technology Development under grant: 101.01-2019.320.

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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

    Duong Viet Thong

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

    Vu Tien Dung

  3. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, South Korea

    Yeol Je Cho

  4. Center for General Education, China Medical University, Taichung, Taiwan, 40404, China

    Yeol Je Cho

Authors
  1. Duong Viet Thong
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  2. Vu Tien Dung
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  3. Yeol Je Cho
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Correspondence to Yeol Je Cho.

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Dedicated to Professor Pham Ky Anh on the occasion of his 70th birthday

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Thong, D.V., Dung, V.T. & Cho, Y.J. A new strong convergence for solving split variational inclusion problems. Numer Algor 86, 565–591 (2021). https://doi.org/10.1007/s11075-020-00901-0

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