Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications


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.


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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


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