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Tseng type methods for solving inclusion problems and its applications

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Abstract

In this paper, we introduce two modifications of the forward–backward splitting method with a new step size rule for inclusion problems in real Hilbert spaces. The modifications are based on Mann and viscosity-ideas. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish strong convergence of the proposed algorithms. We present two numerical examples, the first in infinite dimensional spaces, which illustrates mainly the strong convergence property of the algorithm. For the second example, we illustrate the performances of our scheme, compared with the classical forward–backward splitting method for the problem of recovering a sparse noisy signal. Our result extend some related works in the literature and the primary experiments might also suggest their potential applicability.

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Acknowledgements

The authors would like to thank the referees for their comments on the manuscript which helped in improving earlier version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

  2. The Center for Mathematics and Scientific Computation, University of Haifa, Mt. Carmel, 3498838, Haifa, Israel

    Aviv Gibali

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

    Duong Viet Thong

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  1. Aviv Gibali
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  2. Duong Viet Thong
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Correspondence to Duong Viet Thong.

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Gibali, A., Thong, D.V. Tseng type methods for solving inclusion problems and its applications. Calcolo 55, 49 (2018). https://doi.org/10.1007/s10092-018-0292-1

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