The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which als...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2020; no. 1; pp. 1 - 12
Main Authors: Wang, Yuanheng, Wu, Xiuping, Pan, Chanjuan
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 08.12.2020
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Asymptotically nonexpansive mapping
Differential Geometry
Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Split common fixed point
Strong convergence
Topology
Variational inequality
Split common fixed point
Strong convergence
Asymptotically nonexpansive mapping
Variational inequality
ISSN:1687-1812, 1687-1812
Online Access:Get full text
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Summary:In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.
ISSN:1687-1812
1687-1812
DOI:10.1186/s13663-020-00686-w