[PDF] Top 20 Strong convergence of a new general iterative method for variational inequality problems in Hilbert spaces

... Lemma 2.9. Let C be a closed convex subset of a Hilbert space H. Let S : C ® C be a non-expansive mapping and j be an MKC on C. Suppose F: C ® C be a h-strongly monotone and L-Lipschitzian mapping with coefficient ... See full document

... a new iterative algorithm for approximating a common solution of certain class of multiple–sets split variational inequality ...proposed iterative algorithm is proved to converge ... See full document

... Banach spaces with a Fr´ehet differentiable ...fundamental convergence results. However, this scheme has only weak convergence even in a Hilbert space ...have strong convergence; ... See full document

... classical variational inequality ...for variational inequality problems and fixed point set of nonexpansive ...mappings. Strong convergence theorems are established in the ... See full document

... approximation method for solving common solutions of variational inequality and fixed point ...problems. Strong convergence theorems are established in the framework of ... See full document

... equilibrium problems have been considered by many authors; see, for example, 6, 8–19 and the reference ...equilibrium problems and few of authors investigate the infinite family of equilibrium ... See full document

... real Hilbert space, and B : H H be a set-valued mapping with domain D(B) := {x ∈ H : B(x) = ...well-known method for approximating a zero point of a maximal monotone mapping defined in a real Hilbert ... See full document

... the variational inequality γ f ( q ) − Aq , q − p ≤ 0, ∀ p ∈ F , where F = F ( S ) ∩ EP ( B ) and is also the optimality con- dition for the minimization problem min x ∈ F (1/2) Ax,x − h(x), where h is a ... See full document

... a new general iterative scheme for finding a common element of the set of solutions of variational inequality problem for an inverse-strongly monotone mapping and the set of fixed ... See full document

... a new system of general variational inequalities in Banach ...of variational inequalities and fixed point problems concerning the nonexpansive mapping is ...an iterative scheme ... See full document

... a general iterative algorithm, we study the problem of approx- imating a common element in the common fixed point set of an infinite family of non- expansive mappings, in the solution set of a ... 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

... real Hilbert space, and B be a set-valued mapping with domain D(B) := { x ∈ H : B(x) = ∅} ...well-known method for approximating a zero point of a maximal monotone mapping defined in a real Hilbert ... See full document

... to variational inclusion, equilibrium and fixed point problems have been recently extensively investigated based on iterative methods; see [–] and the ref- erences ...complex problems, which ... See full document

... Numerous problems in physics, optimization, and economics reduce to find a solution of equilibrium ...equilibrium problems in Hilbert space, see, for instance, Blum and Oettli 1, Combettes and ... See full document

... minimization problems; see, for example, 5–8 and the references ...minimization problems have a great impact and influence in the development of almost all branches of pure and applied ... See full document

... an iterative algorithm for finding such a solution is constructed, and convergent theorem of the such algorithm is ...assume strong monotonicity of general variational inequality ... 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

... norm, are denoted by ,   and  , respectively. Let C be a nonempty closed convex subset of H, and let B: C  H be a nonlinear map. The classical variational inequality which is denoted by VI(C,B) is to ... 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