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Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings

Author

Listed:
  • Bing Tan

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Zheng Zhou

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Songxiao Li

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.

Suggested Citation

  • Bing Tan & Zheng Zhou & Songxiao Li, 2020. "Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings," Mathematics, MDPI, vol. 8(4), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:462-:d:336957
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    References listed on IDEAS

    as
    1. Bing Tan & Shanshan Xu & Songxiao Li, 2020. "Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    2. Xiaolong Qin & Nguyen Thai An, 2019. "Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets," Computational Optimization and Applications, Springer, vol. 74(3), pages 821-850, December.
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