Geodesic
Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications :
Tang, Yuchao 1   ; Zong, Chunxiang 1
1 Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 12, p. 5980-5994 Cet article a éte moissonné depuis la source International Scientific Research Publications

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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.

DOI : 10.22436/jnsa.009.12.06
Classification : 47H10, 90C25
Keywords: Common fixed point, nonexpansive mappings, minimum-norm, cyclic iteration method, simultaneous iteration method.

Tang, Yuchao  1   ; Zong, Chunxiang  1

1 Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China 
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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 its applications, Tome 9 (2016) no. 12, p. 5980-5994. doi: 10.22436/jnsa.009.12.06

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