[PDF] Top 20 Variational inequality problems in H spaces

... an inequality associated with the variational inequality or variational-type ...The variational inequality problem is to find x 0 ∈ K such that T (x 0 ), v − x 0 ∈ ... See full document

... is not properly contained in the graph of any other monotone mapping. It is generally known that M is maximal if and only if for (x, u) ∈ H ×H, hx −y, u− vi ≥ 0 for all (y, v) ∈ G(M ) implies u ∈ M (x). A ... See full document

... Theorem 1.1 (see Nadezhkina and Takahashi [8]). Let C be a nonempty closed convex sub- set of a real Hilbert space H . Let A : C → H be a monotone k-Lipschitz continuous mapping, and let S : C → C be a ... See full document

... lower semi-continuity of the solution of PIVEP in locally convex Hausdorff topological vector spaces. This paper is motivated and inspired by the recent paper [] and its aim is to extend the results to the setting ... See full document

... The goal of this paper is to introduce a split-type problem, by combining a split fixed point problem and a hierarchical variational inequality problem. The considered problem can be applied to solve many ... See full document

... First we recall that a mapping f : C → C is a contraction on C if there exists a constant k ∈ 0, 1 such that f x − fy ≤ kx − y, x, y ∈ C. A mapping T : C → C is called nonexpansive if Tx − Ty ≤ x − y, x, y ∈ C. We denote ... See full document

... 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 ... See full document

... In this paper, we introduce an iterative process which converges strongly to a common solution of a finite family of variational inequality problems for monotone mappings with Bregman distance ... See full document

... We introduced a new iterative scheme for finding a common element in the set of common fixed points of a finite family of quasi-φ-nonexpansive mappings, the set of common solutions of a finite family of equilibrium ... See full document

... hierarchical variational inclusion problems in the setting of Hilbert ...programming problems and quadratic minimization problems by using the main ... See full document

... Corollary 3.3. Let H be a real Hilbert space and C be a nonempty closed convex subset of H. S a finite family of nonexpansive mappings from C into itself and F : C × C → R a bifunction satisfying (A1)–(A4). ... See full document

... Hilbert spaces. Variational inequalities and fixed point problems of quasi-nonexpansive mappings are also considered as applications of the main ... See full document

... Corollary 3.2. Let C be a nonempty closed convex subset of a Hilbert space H. Let Θ be a bifunction from C × C to R satifies (A1)–(A4). Let T be a k-strictly pseudocontractive mapping of C into itself. Let f be a ... See full document

... 36. Wittmann, R: Approximation of fixed points of non-expansive mappings. Arch. Math. 58, 486-491 (1992) 37. Moudafi, A: Viscosity approximation methods for fixed-points problems. J. Math. Anal. Appl. 241, 46-55 ... See full document

... : H → H be a contraction with coefficient 0 < α < ...: H → H be strongly positive linear bounded mapping with coefficient η ∈ 0, 1 and β > 0, ... See full document

... This paper has improved the iterative method of Wu and Huang [] for solving generalized variational inequality problem (.), several results regarding the generalized proximity operator and its relations ... See full document

... the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi- nonexpansive mappings in a Banach ... See full document

... We design synchronal algorithm and cyclic algorithm based on the general iterative algorithm proposed by Tian in 2010 for finding the common fixed point x * of finite family of strict pseudo-contractive mappings which is ... See full document

... Banach spaces has many applications in nonlinear partial differential equations, nonlinear semi-group theory, variational inequality and so on (see ...Banach spaces has been well de- ...Banach ... See full document

... Dafermos in [7] utilized the fixed-point technique to ponder the sensitivity analysis of Stampacchia’s variational inequalities. Time to time the model has been changed and stretched out by numerous writers for ... See full document