On the strong convergence of a general-type Krasnosel’skii–Mann’s algorithm depending on the coefficients

Let H be a Hilbert space, ( W n ) n ∈ N a suitable family of mappings, S a nonexpansive mapping and D a strongly monotone operator. We are interested in the strong convergence of the general scheme x n + 1 = γ x n + ( 1 - γ ) W n ( α n S x n + ( 1 - α n ) ( I - μ n D ) x n ) , γ ∈ [ 0 , 1 ) , in dep...

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Published in:Fixed point theory and algorithms for sciences and engineering Vol. 18; no. 1; pp. 1 - 25
Main Authors: Hussain, Newab, Marino, Giuseppe, Muglia, Luigi, Abdou, Afrah A. N.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2016
Springer Nature B.V
Subjects:
Analysis
Convergence
Hilbert space
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
strongly monotone operators
58E35
47H10
47H09
variational inequality
Iterative methods
65J25
nonexpansive mappings
ISSN:1661-7738, 1661-7746, 2730-5422
Online Access:Get full text
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Summary:Let H be a Hilbert space, ( W n ) n ∈ N a suitable family of mappings, S a nonexpansive mapping and D a strongly monotone operator. We are interested in the strong convergence of the general scheme x n + 1 = γ x n + ( 1 - γ ) W n ( α n S x n + ( 1 - α n ) ( I - μ n D ) x n ) , γ ∈ [ 0 , 1 ) , in dependence of the coefficients ( α n ) n ∈ N and ( μ n ) n ∈ N .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1661-7738
1661-7746
2730-5422
DOI:10.1007/s11784-015-0261-0