Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications
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Authors
Yuchao Tang
- Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China.
Chunxiang Zong
- Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China.
Abstract
This paper deals with iterative methods for approximating the minimum-norm common fixed point of
nonexpansive mappings. The proposed cyclic iterative algorithms and simultaneous iterative algorithms
combined with a relaxation factor, which make them more
flexible to solve the considered problem. Under
certain conditions on the parameters, we prove that the sequences generated by the proposed iteration
scheme converge strongly to the minimum-norm common fixed point of a finite family of nonexpansive
mappings. Furthermore, as applications, we obtain several new strong convergence theorems for solving
the multiple-set split feasibility problem which has been found application in intensity modulated radiation
therapy. Our results extend and improve some known results in the literature.
Share and Cite
ISRP Style
Yuchao Tang, Chunxiang Zong, Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 5980--5994
AMA Style
Tang Yuchao, Zong Chunxiang, Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications. J. Nonlinear Sci. Appl. (2016); 9(12):5980--5994
Chicago/Turabian Style
Tang, Yuchao, Zong, Chunxiang. "Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 5980--5994
Keywords
- Common fixed point
- nonexpansive mappings
- minimum-norm
- cyclic iteration method
- simultaneous iteration method.
MSC
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