Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications

Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications

“…So, when we study the solution of MEP, we only need to study the solution of the equilibrium (1.1). This also shows that some "so-called" mixed equilibrium problem studied in [15][16][17] is still the equilibrium problem (1.1).…”

“…The problem MEP studied in [15][16][17] and the problem GEP studied in [18][19][20] are still the problem (1.1) studied in the literature [5][6][7][8][9][10][11][21][22][23][24] and others.…”

“…Remark 4.1 Recently, some authors introduced the following mixed equilibrium problem (MEP, for short) (see [15][16][17] and references therein) and generalized equilibrium problem (GEP, for short) (see [18][19][20] and references therein):…”

“…In [15][16][17], the authors gave some iterative methods for finding the solution of MEP when the bi-function f(x, y) admits the conditions (A1)-(A4) and the real-valued function satisfies the following condition:…”

Triple Hierarchical Variational Inequalities with Constraints of Mixed Equilibria, Variational Inequalities, Convex Minimization, and Hierarchical Fixed Point Problems

“…with > 0 a given number, which is known as the extragradient method. The literature on the VIP is vast, among which, Korpelevich's extragradient method has received great attention in various applications and undergone improvements in many ways; see, for example, [7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein, to name but a few. Let : → R be a real-valued function, let : → be a nonlinear mapping, and let Θ : × → R be a bifunction.…”