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Convergence theorems by extragradient method in Banach spaces (1509.02018v3)
Published 7 Sep 2015 in math.FA
Abstract: In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly monotone operator and fixed points of two relatively nonexpansive mappings in Banach spaces. We prove strong convergence theorems by this method under suitable conditions. A numerical example is given to illustrate the usability of our results.