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Parallel extragradient-proximal methods for solving split system of fixed point set constraint equilibrium problem in real Hilbert space -by Anteneh Getachew Gebrie and Rabian Wangkeeree

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Abstract: In this paper, we propose two parallel extragradient-proximal methods for solving finite family of split equilibrium problems and split common fixed point problems, we call the problem split system of fixed point set constraint equilibrium problem (SSFPSCEP). The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. To obtain the strong convergence, we combine the first algorithm with the shrinking projection method in the second algorithm. Finally, appplication and one numerical experiment is given to demonstrate the efficiency of our algorithms.

Keywords: Common fixed point problem, Split equilibrium problem, Lipschitz-type continuous bifunction, Proximal method, Monotone bifunction, Shrinking projection method, Extragradient method.

DOI: https://doi.org/10.30697/rfpta-2018-011

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How to cite this article: Anteneh Getachew Gebrie and Rabian Wangkeeree, Parallel Extragradient-Proximal Methods for solving split system of fixed point set constraint equilibrium problem in real Hilbert space, vol. 2018, Article ID 2018011, 26 pages, 2018.

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Copyright © 2018 SUMA Publishing Group., This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.