A New Approximation Scheme Combining the Viscosity Method with Extragradient Method for Mixed Equilibrium Problems
Jian-Wen Peng, Soon‐Yi Wu · Fixed Point Theory and Applications · 2010
Abstract We introduce a new approximation scheme combining the viscosity method with extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings and the set of the variational inequality for a monotone, Lipschitz continuous mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend, and improve some well-known results in the literature.