Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings

Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings

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 sm...

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Bibliographic Details
Main Authors: Najla Altwaijry, Tahani Aldhaban, Souhail Chebbi, Hong-Kun Xu
Format: Article
Language:English
Published: MDPI AG 2020-07-01
Series:Mathematics
Subjects:
nonexpansive mapping
Krasnoselskii–Mann
viscosity approximation method
strong convergence
uniformly smooth Banach space
Online Access:https://www.mdpi.com/2227-7390/8/7/1153
Description
Summary: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.
ISSN:2227-7390

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