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Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments

Author

Listed:
  • Li Wei

    (School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China)

  • Yibin Xin

    (School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China)

  • Ruilan Zhang

    (School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA)

Abstract

In this paper, some new modified inertial-type multi-choice CQ-algorithms for approximating common fixed point of countable weakly relatively non-expansive mappings are presented in a real uniformly convex and uniformly smooth Banach space. New proof techniques are used to prove strong convergence theorems, which extend some previous work. The connection and application to maximal monotone operators are demonstrated. Numerical experiments are conducted to illustrate that the rate of convergence is accelerated compared to some previous ones for some special cases.

Suggested Citation

  • Li Wei & Yibin Xin & Ruilan Zhang & Ravi P. Agarwal, 2020. "Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments," Mathematics, MDPI, vol. 8(4), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:613-:d:346337
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    References listed on IDEAS

    as
    1. Jingling Zhang & Yongfu Su & Qingqing Cheng, 2012. "Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, November.
    2. Boţ, Radu Ioan & Csetnek, Ernö Robert & Hendrich, Christopher, 2015. "Inertial Douglas–Rachford splitting for monotone inclusion problems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 472-487.
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