Inertial Krasnosel’skiǐ–Mann type hybrid algorithms for solving hierarchical fixed point problems

In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 21; no. 2; pp. 1 - 22
Main Authors: Dong, Qiao-Li, Kazmi, K. R., Ali, Rehan, Li, Xiao-Huan
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2019
Springer Nature B.V
Subjects:
Algorithms
Analysis
Convergence
Fixed points (mathematics)
Hilbert space
Iterative methods
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
49J35
inertial Krasnosel’skiǐ–Mann type hybrid algorithm
47H10
90C47
Hierarchical fixed point problem
nonexpansive mapping
strong convergence
ISSN:1661-7738, 1661-7746, 2730-5422
Online Access:Get full text
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Summary:In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak comparing other algorithms for the hierarchical fixed point problems. Further, we derive some consequences from the main results. Finally, we present two academic numerical examples for comparing these two algorithms with the algorithm in Dong et al. (J Fixed Point Theory A 19(4):3097–3118, 2017 ), which illustrate the advantage of the proposed algorithms. The methods and results presented in this paper generalize and unify previously known corresponding methods and results of this area.
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ISSN:1661-7738
1661-7746
2730-5422
DOI:10.1007/s11784-019-0699-6