Iterative algorithms for finding minimumnorm 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 minimumnorm 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 minimumnorm common fixed point of a finite family of nonexpansive
mappings. Furthermore, as applications, we obtain several new strong convergence theorems for solving
the multipleset 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 minimumnorm fixed point of a finite family of nonexpansive mappings and applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 59805994
AMA Style
Tang Yuchao, Zong Chunxiang, Iterative algorithms for finding minimumnorm fixed point of a finite family of nonexpansive mappings and applications. J. Nonlinear Sci. Appl. (2016); 9(12):59805994
Chicago/Turabian Style
Tang, Yuchao, Zong, Chunxiang. "Iterative algorithms for finding minimumnorm fixed point of a finite family of nonexpansive mappings and applications." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 59805994
Keywords
 Common fixed point
 nonexpansive mappings
 minimumnorm
 cyclic iteration method
 simultaneous iteration method.
MSC
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