[PDF] Top 20 Monotone variational inequalities, generalized equilibrium problems and fixed point methods

... that variational inequality ...fixed point problem. The element x ∈ C is a solution of variational inequality ...fixed point equation x = Proj C (x – λAx), where λ >  is a ...of ... See full document

... Motivated and inspired by Ceng and Yao [] and Yang et al. [], the purpose of this paper is to introduce two hybrid algorithms for the variational inequalities and mixed equilibrium problems ... See full document

... converges weakly to a point, which lies in VI(C, A). The literature on the VIP is quite vast and Korpelevich’s extragradient method, which is projection-based, has received great at- tention given by many ... See full document

... the generalized mixed equilibrium problem ...a variational inclusion (.), and the set of solutions of the generalized mixed equilibria problem ... See full document

... invex equilibrium problem related to the original ...fixed point, which is the solution of the original ...iterative methods for solving various classes of equilibrium problems, ... See full document

... hierarchical variational inequality problem de- fined over the set of solutions of a variational inequality problem which is defined over the intersection of the set of common fixed points of a sequence of ... See full document

... In this paper, we propose a new iterative scheme for finding a solution of SMVIP (1.3) with the constraints of a variational inequality and a fixed point problem of a finite family of strict ... See full document

... Recently, Plubtieng and Punpaeng [] and Ceng et al. [, ] considered some iterative methods for VIP (.) and its extended versions and got some strong convergence theo- rems. As a generalization of VIP ... See full document

... Fixed point theory has played important roles in traditional equilibrium theory, varia- tional inequalities and optimization theory (see ...[–]). Fixed point theorems have ... See full document

... the equilibrium problems are unified models of several prob- lems, namely, optimization problems, saddle point problems, variational inequalities, fixed point ... See full document

... hierarchical fixed point approach to variational inequalities,” Bulletin of the Australian Mathematical Society, ...hierarchical fixed-point problems,” Pacific Journal of ... See full document

... common fixed point of a family of nonexpansive mappings has been studied by many ...a point in the intersection of the fixed point sets of a family of nonexpansive mapping see 6, ... See full document

... split generalized equilibrium problem reduces to the gener- alized equilibrium problem considered by Cianciaruso et ...split generalized equilibrium problem reduces to the split ... See full document

... inclusion problems, saddle point problems, variational inequality problems, minimization problems, the Nash equilibria in noncooperative games, vector equilibrium ... See full document

... of variational inclusions for maximal monotone and inverse-strongly monotone mappings with the constraints of two problems: a gener- alized mixed equilibrium problem and a common fixed ... See full document

... fixed point problem (.) links with some mono- tone variational inequalities and convex programming problems; see ...fixed point problem; see ... See full document

... Very recently, based on Yamada’s hybrid steepest-descent method [] and Colao, Marino, and Xu’s hybrid viscosity approximation method [], Ceng et al. [] introduced a hybrid iterative method for finding a common element ... See full document

... paper, fixed point problems of nonexpansive mappings and solution problems of generalized variational inequalities are investigated based on a viscosity approximate ... See full document

... Korpelevich’s extragradient method has extensively been studied in the literature for solving a more general problem that consists of finding a common point that lies in the solution set of a variational ... See full document

... of fixed points of a family of finitely nonexpansive mappings, the set of solutions of mixed equilibrium problem and the set of solutions of a variational inequality problem for a β-inverse-strongly ... See full document