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Volume 11, Issue 4
Weak and Strong Convergence of Two Algorithms for the Split Fixed Point Problem

Fenghui Wang & Hong-Kun Xu

DOI: 10.4208/nmtma.2018.s05

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 770-781.

Published online: 2018-06

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  • Abstract

Two iterative algorithms are proposed for the split fixed point problem. The first algorithm is shown to be weakly convergent and the second one to be strongly convergent. One feature of these algorithms is that the step sizes are chosen in such a way that no priori knowledge of the operator norms is required. A new idea is introduced in order to prove strong convergence of the second algorithm.

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@Article{NMTMA-11-770, author = {Fenghui Wang and Hong-Kun Xu}, title = {Weak and Strong Convergence of Two Algorithms for the Split Fixed Point Problem}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {4}, pages = {770--781}, abstract = {

Two iterative algorithms are proposed for the split fixed point problem. The first algorithm is shown to be weakly convergent and the second one to be strongly convergent. One feature of these algorithms is that the step sizes are chosen in such a way that no priori knowledge of the operator norms is required. A new idea is introduced in order to prove strong convergence of the second algorithm.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2018.s05}, url = {http://global-sci.org/intro/article_detail/nmtma/12471.html} }
TY - JOUR T1 - Weak and Strong Convergence of Two Algorithms for the Split Fixed Point Problem AU - Fenghui Wang & Hong-Kun Xu JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 770 EP - 781 PY - 2018 DA - 2018/06 SN - 11 DO - http://doi.org/10.4208/nmtma.2018.s05 UR - https://global-sci.org/intro/article_detail/nmtma/12471.html KW - AB -

Two iterative algorithms are proposed for the split fixed point problem. The first algorithm is shown to be weakly convergent and the second one to be strongly convergent. One feature of these algorithms is that the step sizes are chosen in such a way that no priori knowledge of the operator norms is required. A new idea is introduced in order to prove strong convergence of the second algorithm.

Fenghui Wang and Hong-Kun Xu. (2018). Weak and Strong Convergence of Two Algorithms for the Split Fixed Point Problem. Numerical Mathematics: Theory, Methods and Applications. 11 (4). 770-781. doi:10.4208/nmtma.2018.s05
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