Abstract
The purpose of this paper is to introduce a new hybrid relaxed extragradient iterative method for finding a common element of the solution of set a equilibrium, variational inequality and the set of fixed point of a \(\xi \)-strict pseudocontraction mapping in Hilbert spaces. We obtain a strong convergence theorem of the purposed iterative algorithm under some suitable conditions. The results presented in this paper generalize, improve and extend some well-known results in the literature.
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Acknowledgments
The authors were supported by the Higher Education Research Promotion and National Research University Project of Thailand, Office of the Higher Education Commission (NRU-CSEC No. 55000613).
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Phiangsungnoen, S., Kumam, P. (2014). A New Hybrid Relaxed Extragradient Algorithm for Solving Equilibrium Problems, Variational Inequalities and Fixed Point Problems. In: Yang, GC., Ao, SI., Huang, X., Castillo, O. (eds) Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 275. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7684-5_26
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DOI: https://doi.org/10.1007/978-94-007-7684-5_26
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