[PDF] Top 20 Strong convergence of extragradient method for generalized variational inequalities in Hilbert space

... Hilbert space. Let X be a nonempty, closed and convex subset of the Hilbert space ...The generalized variational inequality problem, abbreviated as GVIP, is to find a vector x ∗ ∈ ... See full document

... linear variational inequalities and established strong convergence ...nonlinear variational inequalities involving two different nonlinear operators and estab- lished ... See full document

... the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of a nonexpansive mapping, and the set of solutions ... See full document

... a variational inequality. Several strong convergence results for the sequences generated by these iterative schemes are established in Hilbert ...two generalized variational ... See full document

... hybrid extragradient viscosity iterative algorithm for finding a common element of the set of solutions of a general mixed equilibrium problem, the set of solutions of a general system of variational ... See full document

... “An extragradient method for fixed point problems and variational inequality problems,” Journal of Inequalities and Applications, ...“Strong convergence theorems for a ... See full document

... same strong convergence conclusion as in Huang’s result ...geometric convergence rate estimate for approximate ...solving variational inclusions have been further studied and developed; for ... See full document

... hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive ... See full document

... descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and Optimization and Their ... See full document

... Lemma 2.7 Let F be a L-Lipschitzian and h-strongly monotone operator on a none- mpty closed convex subset C of a real Hilbert space H with 0 <h ≤ L and 0 <t < 2h/ L 2 . Then S = (I - tF): C ® C is ... See full document

... Variational inequalities are one of the most interesting and intensively studied classes of mathematical problems and there exists a considerable amount of literature [–] on the approximate solvability ... See full document

... a Hilbert space, problem ...problems, variational inequalities, minimax problems, the Nash equilibrium problem in noncooperative games and others; see, for example, ... See full document

... Theorem 1. Let C be a nonempty closed convex subset of a real Hilbert space H. Let A : C ® H be a monotone and k-Lipschitz continuous mapping. Let S : C ® C be a uniformly continuous asymptotically ... See full document

... split variational inclusion problem and give several strong convergence theorems in Hilbert spaces, like the Halpern-Mann type iteration method, the regularized iteration ...give ... See full document

... real Hilbert space; Marino and Xu [] proved a strong convergence theorem for strict- pseudo-contractions in a real Hilbert space; Zhou [] extended Marino and Xu’s ... See full document

... the variational inequality ...the generalized projection operator in uniformly convex and uniformly smooth Ba- nach spaces, Li [1] established the convergence of a Mann type iterative scheme for ... See full document

... regularization method for seeking a solution to a class of monotone variational inequalities in a real Hilbert space, where the regularizer is a hemicontinuous and strongly monotone ... See full document

... the generalized equilibrium problem, and the set of solutions of variational inequality problem for a relaxed u, v-cocoercive mapping in a real Hilbert ... See full document

... the strong conver- gence approximation scheme for finding a com- mon element of the set of solutions of a system of an equilibrium problem and the set of common fixed points of a sequence of nonexpansive map- ... See full document

... classical variational inequality problem ...hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of problem ... See full document