Abstract
In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence of the iterates generated by each method is obtained under assumptions that the fixed point mapping is quasi-nonexpansive and demiclosed at 0, and the bifunction associated with the equilibrium problem is weakly continuous. The bifunction is assumed to be satisfying a Lipschitz-type condition when the basic iteration comes from the extragradient method. It becomes unnecessary when an Armijo back tracking linesearch is incorporated in the extragradient method.
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Acknowledgments
The authors would like to thank the referees for their helpful comments and remarks which helped them very much in revising the paper. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2A10008908). The first author is supported by NAFOSTED, under the Project 101.01-2014-24.
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Dinh, B.V., Kim, D.S. Extragradient algorithms for equilibrium problems and symmetric generalized hybrid mappings. Optim Lett 11, 537–553 (2017). https://doi.org/10.1007/s11590-016-1025-5
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DOI: https://doi.org/10.1007/s11590-016-1025-5