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Three new iterative methods for solving inclusion problems and related problems

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Abstract

In this paper, we study the variational inclusion problem which consists of finding zeros of the sum of a single and multivalued mappings in real Hilbert spaces. Motivated by the viscosity approximation, projection and contraction and inertial forward–backward splitting methods, we introduce two new forward–backward splitting methods for solving this variational inclusion. We present weak and strong convergence theorems for the proposed methods under suitable conditions. Our work generalize and extend some related results in the literature. Several numerical examples illustrate the potential applicability of the methods and comparisons with related methods emphasize it further.

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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

  4. Department of Mathematics, University of Transport and Communications, Hanoi, Vietnam

    Nguyen The Vinh

Authors
  1. Aviv Gibali
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  2. Duong Viet Thong
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  3. Nguyen The Vinh
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Correspondence to Duong Viet Thong.

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Communicated by José R Fernández.

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Gibali, A., Thong, D.V. & Vinh, N.T. Three new iterative methods for solving inclusion problems and related problems. Comp. Appl. Math. 39, 187 (2020). https://doi.org/10.1007/s40314-020-01215-6

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  • DOI: https://doi.org/10.1007/s40314-020-01215-6

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