A viscosity extragradient method for an equilibrium problem and fixed point problem in Hilbert space

Extragradient Method for Fixed Points in CAT(0) Spaces

“…Remark 27. Our Theorem 21 is an analog of Theorem 3.1 of Wang et al [30] for the Hilbert space case.…”

Parallel extragradient algorithms for a family of pseudomonotone equilibrium problems and fixed point problems of nonself-nonexpansive mappings in Hilbert space

“…Recently, some authors modified the hybrid methods to find solutions of pseudomonotone equilibrium problems; see, e.g., [12,14,15,16,17]. Wang et al [18] considered a viscosity extragradient method to find a common element of the solution set of a pseudomonotone equilibrium problem and the fixed point set of a nonexpansive mapping as follows:…”

Convergence Theorems for Generalized Viscosity Explicit Methods for Nonexpansive Mappings in Banach Spaces and Some Applications

“…for any x 0 ∈ H, where {t n } ∞ n=1 ⊂ (0, 1) is a sequence. On the other hand, since, in 2000, Moudafi [9] introduced viscosity approximation methods for fixed point problems in Hilbert spaces, some authors have obtained some convergence theorems of viscosity approximation methods to show the existence of fixed points of some kinds of nonlinear mappings and solutions of nonlinear problems (see, for example, [10][11][12][13][14][15][16][17][18][19][20]). Especially, in 2015, Xu et al [8] combined the Moudafi viscosity method [9] with the implicit midpoint method for a nonexpansive mapping in Hilbert spaces as follows:…”