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Open AccessArticle

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

1
School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China
2
Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 613; https://doi.org/10.3390/math8040613
Received: 13 March 2020 / Revised: 8 April 2020 / Accepted: 9 April 2020 / Published: 16 April 2020
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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. View Full-Text
Keywords: Lyapunov functional; weakly relatively non-expansive mapping; monotone operator; inertial-type algorithm; multi-choice CQ-algorithm; common fixed point Lyapunov functional; weakly relatively non-expansive mapping; monotone operator; inertial-type algorithm; multi-choice CQ-algorithm; common fixed point
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Wei, L.; Xin, Y.; Zhang, R.; Agarwal, R.P. Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments. Mathematics 2020, 8, 613.

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