[PDF] Top 20 An iterative method for nonexpansive semigroups, variational inclusions and generalized equilibrium problems

... where θ is a zero vector in H. The set of solutions to variational inclusion (1.1) is denoted by I(A, M). When A = 0, then (1.1) becomes the inclusion problem introduced by Rockafellar [1]. Let ϕ : C → H be a ... See full document

... general iterative method (.) to the case of non- expansive semigroups and equilibrium ...of nonexpansive mappings, Shehu [] proposed an iterative method for ... See full document

... an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse strongly ... See full document

... 5. Lions, JL, Stampacchia, G: Variational inequalities. Commun. Pure Appl. Math. 20, 493-517 (1967) 6. Yao, JC: Variational inequalities with generalized monotone operators. Math. Oper. Res. 19, ... See full document

... the iterative scheme ...three-step iterative scheme in [, Algorithm I] to the four-step iterative scheme for THVIP ...extragradient method, the viscosity approximation method, the ... See full document

... steepest-descent method for solving the VI(F, C). Assume that F is an η-strongly mono- tone and κ-Lipschitzian mapping with κ > , η >  on C. An equally important problem is how to find an approximate ... See full document

... operator on H (i.e., there is a constant γ > ¯ 0 such that Ax, x ≥ ¯ γ x 2 , ∀x Î H) and h is a potential function for g f (i.e., h’(x) = g f(x) for all x Î H). For this kind of optimi- zation problems, see, ... See full document

... a finite family of nonexpansive mappings from C into itself and F : C × C → R a bifunction satisfying (A1)–(A4). Let A : C → H be relaxed u, v-cocoercive and μ-Lipschitzian. Let f : C → C be an α-contraction with ... See full document

... It is well known that the hierarchical fixed point problem (.) links with some mono- tone variational inequalities and convex programming problems; see []. Various meth- ods have been proposed to solve ... See full document

... new method for a system of generalized equilibrium problems, system of variational inequality problems, and fixed point problems by using S-mapping generated by a finite ... 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

... two iterative algorithms for find- ing common solutions of a finite family of variational inclusions for maximal monotone and inverse-strongly monotone mappings with the constraints of two ... See full document

... an iterative scheme for finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal ... See full document

... It is known that the hierarchical fixed point problem (.) links with some monotone vari- ational inequalities and convex programming problems; see []. Various methods have been proposed to solve the ... See full document

... (I - A))(q). By Lemma 2.2 we obtain that 〈(gf - A)q, w - q〉 ≤ 0 for all w Î Θ. Next, we show that lim sup n→∞ ( γ f − A)q, Sy n − q ≤ 0, where q = P Θ (gf + I - A) (q) is the unique solution of the variational ... See full document

... mixed equilibrium problem, quasivariational inclusion problem, and fixed point problem of nonexpansive semigroup,” Journal of Inequalities and Applications, ... See full document

... general iterative scheme for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup, the set of solutions of the generalized mixed equilibrium ... See full document

... Theorem 3.1. Let C be a nonempty closed convex subset of a real Hilbert space H, let F : C× C → R be a bifunction satisfying (A1)–(A5), let ϕ : C → R ∪ {∞} be a proper lower semicontinuous and convex function, let A : H ... See full document

... an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of generalized equilibrium problems, the set of common fixed points of ... See full document

... complementarity, variational inequalities, optimal control, mathematical economics, equilibria, and game ...of variational inclusions problems have been extended and ...new iterative ... See full document