Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings

Najla Altwaijry, Tahani Aldhaban, Souhail Chebbi and Hong-Kun Xu
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Najla Altwaijry: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Tahani Aldhaban: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Souhail Chebbi: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Hong-Kun Xu: School of Science, Hangzhou Dianzi University, Hangzhou 310018, China

Mathematics, 2020, vol. 8, issue 7, 1-9

Abstract: 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.

Keywords: nonexpansive mapping; Krasnoselskii–Mann; viscosity approximation method; strong convergence; uniformly smooth Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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