Convergence theorem for equilibrium problem and Bregman strongly nonexpansive mappings in Banach spaces

Strong convergence theorem for a system of generalized mixed equilibrium problems and finite family of Bregman nonexpansive mappings in Banach spaces

“…In addition, if f : E → (−∞, +∞] is a proper lower semicontinuous function, then f * : E * → (−∞, +∞] is a proper weak * lower semicontinuous and convex function (see [17]). Hence, V f is convex in the second variable.…”

An extragradient algorithm for split generalized equilibrium problem and the set of fixed points of quasi-φ-nonexpansive mappings in Banach spaces

“…The problem of finding a common element of the set of fixed points of a nonlinear mapping and the solution set of an equilibrium problem have been studied by many authors in the framework of the Hilbert spaces and Banach spaces (see [9,18,25,29,34]). In solving problems of this type when pseudomonotone bifunction is involved, there have been several works in the framework of Hilbert spaces where linesearch algorithms have been employed.…”

Existence of equilibrium for generalized games in choice form and applications

“…The importance of vector equilibrium problems comes, obviously, from the great number of recent papers dedicated to the study of the existence of their solutions. We can provide a short list of references presented in our bibliography: [1][2][3][4][5], [7], [9], [10], [14][15][16][17][18], [21][22][23][24][25], [29]. From the scientific point of view, we must state the fact that the vector equilibrium problems unifies several problems, among which we can mention: vector variational inequalities, vector complementarity problems and vector optimizations problems.…”