A new iteration technique for nonlinear operators as concerns convex programming and feasibility problems

The aim of this work is to develop an S -iteration technique for finding common fixed points for nonself quasi-nonexpansive mappings in the framework of a uniformly convex Banach space. Convergence properties of the proposed algorithm are analyzed in the setting of uniformly convex Banach spaces. To...

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Bibliographic Details
Published in:Numerical algorithms 2020-02, Vol.83 (2), p.421-449
Main Authors: Sahu, D. R., Pitea, A., Verma, M.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Banach spaces
Computer Science
Convexity
Feasibility
Hilbert space
Iterative methods
Numeric Computing
Numerical Analysis
Operators
Original Paper
Theory of Computation
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Summary:The aim of this work is to develop an S -iteration technique for finding common fixed points for nonself quasi-nonexpansive mappings in the framework of a uniformly convex Banach space. Convergence properties of the proposed algorithm are analyzed in the setting of uniformly convex Banach spaces. To prove the usability of our results, some novel applications are provided, focused on zeros of accretive operators, convex programming, and feasibility problems. Some numerical experiments with real datasets for Lasso problems are provided.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-019-00688-9