An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems
Adrian Petruşel, Jen-Chih Yao (2009)
Open Mathematics
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In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.