Abstract
The purpose of this paper is to introduce and study Ishikawa iterative algorithms for solving the SFP in the setting of infinite-dimensional Hilbert spaces. The main results presented in this paper improve and extend some recent results done by Xu [Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problems 26 (2010) 105018]. At the end we prove that the accumulation of errors in Ishikawa iterative CQ algorithm is bounded in certain range.
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References
Ishikawa, S.: Fixed point and iteration of a nonexpansive mapping in a Banach spaces. Proc. Amer. Math. Soc. 73, 7365–7371 (1976)
Qin, X., Cho, Y.J., Kang, S.M.: Viscosity approximation methods for generalized equilibrium problems and fixed point with applicatons. Nonlinear Anal. 72, 99–12 (2010)
Xu, H.-K.: Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space. Inverse Problems 26, 105018 (2010)
Xu, H.-K.: Averaged Mapping and the Gradient-Projection Algorithm (in press)
Xu, Y., Liu, Z., Shin Min, K.: Accumulation and conreol of random errors in the Ishikawa iterative process in arbitrary Banach space. Comput. Math. Appl.
Hundal, H.: An alternating projection that does not converge in norm. Nonlinear Anal. 57, 35–61 (2004)
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Dingping, W., Qibin, D., Erli, W., Hang, Z. (2013). The Split Feasibility Problem in Hilbert Space. In: Yang, G. (eds) Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering. Advances in Intelligent Systems and Computing, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31698-2_161
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DOI: https://doi.org/10.1007/978-3-642-31698-2_161
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31697-5
Online ISBN: 978-3-642-31698-2
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