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

Li Wei, Yibin Xin, Ruilan Zhang and Ravi P. Agarwal
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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

Mathematics, 2020, vol. 8, issue 4, 1-21

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.

Keywords: Lyapunov functional; weakly relatively non-expansive mapping; monotone operator; inertial-type algorithm; multi-choice CQ-algorithm; common fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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