A hybrid extragradient method for approximating the common solutions of a variational inequality, a system of variational inequalities, a mixed equilibrium problem and a fixed point problem

Common Solution to Generalized Mixed Equilibrium Problem and Fixed Point Problem for a Nonexpansive Semigroup in Hilbert Space

“…Motivated by the work of Ceng et al [3], Xiao et al [15], Cianciaruso et al [5], Kazmi et al [8,9,10], and by the ongoing research in this direction, we suggest and analyze an explicit hybrid relaxed extragradient iterative method for approximating a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup.…”

A New Hybrid Extragradient Iterative Method for Approximating the Common Solutions of a System of Variational Inequalities, a Mixed Equilibrium Problem, and a Hierarchical Fixed Point Problem

“…For the recent applications, numerical techniques, and physical formulation, see . We now have a variety of techniques to suggest and analyze various iterative algorithms for solving the system of variational inequalities (1); see [1,2,7,8,12,14,24,28,30]. We introduce the following definitions which are useful in the following analysis.…”

“…The solution set of (14) is denoted by EP( ). Numerous problems in physics, optimization, and economics reduce to find a solution of (14); see [9,13,25,26]. In 1997, Flåm and Antipin [10] introduced an iterative scheme of finding the best approximation to the initial data when EP( ) is nonempty.…”

A New Computational Technique for Common Solutions between Systems of Generalized Mixed Equilibrium and Fixed Point Problems

“…Numerous problems in physics, optimization, and economics reduce to find a solution of problem (4) (see, e.g., [4][5][6][7][8][9]). Several iterative methods to solve the fixed point problems, variational inequality problems, and equilibrium problems are proposed in the literature (see, e.g., [1][2][3][10][11][12][13][14][15][16][17][18]) and the references therein. Let 1 , 2 : → be two mappings.…”