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Weak and strong convergence results for solving inclusion problems and its applications

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Abstract

In this work, we study splitting methods for inclusion problems in real Hilbert space. The algorithms are inspired by forward-backward splitting method, projection and contraction method, inertial method and a self-adaptive step size. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish convergence results of the proposed algorithms. Finally, we present the application of the proposed algorithms for solving convex minimization problems and variational inequalities.

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Acknowledgements

The Project Supported by Scientific Research Project of Xianyang Normal University (Program No.XSYK17015); The Project Supported by College Students’ Innovative Entrepreneurial Training Plan Program(No.S202010722030).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xianyang Normal University, Xianyang, Shaanxi, China

    Jun Yang, Huali Zhao & Min An

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  1. Jun Yang
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  2. Huali Zhao
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  3. Min An
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Correspondence to Jun Yang.

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Yang, J., Zhao, H. & An, M. Weak and strong convergence results for solving inclusion problems and its applications. J. Appl. Math. Comput. 68, 2803–2822 (2022). https://doi.org/10.1007/s12190-021-01644-4

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  • DOI: https://doi.org/10.1007/s12190-021-01644-4

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