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Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings
Open AccessArticle

Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings

1
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2
School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(7), 1153; https://doi.org/10.3390/math8071153
Received: 22 June 2020 / Revised: 10 July 2020 / Accepted: 11 July 2020 / Published: 14 July 2020
(This article belongs to the Special Issue Nonlinear Analysis and Optimization)
We show that the viscosity approximation method coupled with the Krasnoselskii–Mann iteration generates a sequence that strongly converges to a fixed point of a given nonexpansive mapping in the setting of uniformly smooth Banach spaces. Our result shows that the geometric property (i.e., uniform smoothness) of the underlying space plays a role in relaxing the conditions on the choice of regularization parameters and step sizes in iterative methods. View Full-Text
Keywords: nonexpansive mapping; Krasnoselskii–Mann; viscosity approximation method; strong convergence; uniformly smooth Banach space nonexpansive mapping; Krasnoselskii–Mann; viscosity approximation method; strong convergence; uniformly smooth Banach space
MDPI and ACS Style

Altwaijry, N.; Aldhaban, T.; Chebbi, S.; Xu, H.-K. Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings. Mathematics 2020, 8, 1153. https://doi.org/10.3390/math8071153

AMA Style

Altwaijry N, Aldhaban T, Chebbi S, Xu H-K. Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings. Mathematics. 2020; 8(7):1153. https://doi.org/10.3390/math8071153

Chicago/Turabian Style

Altwaijry, Najla; Aldhaban, Tahani; Chebbi, Souhail; Xu, Hong-Kun. 2020. "Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings" Mathematics 8, no. 7: 1153. https://doi.org/10.3390/math8071153

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