A solution for the non-cooperative equilibrium problem of two person via fixed point theory

Abstract

In this paper, we investigate the non-cooperative equilibrium problem of two person games in the setting of game theory and propose a solution via coupled fixed point results in the context of partial metric spaces. We also realize that our coupled fixed point results can be applied to get a solution of a class of nonlinear Fredholm type integral equations. MSC: 46J10; 46J15; 47H10

Split Systems of Nonconvex Variational Inequalities and Fixed Point Problems on Uniformly Prox-Regular Sets

“…Let us take (x * , y * ) ∈ Ξ Fix(S). Since conditions (8) and (13) are satisfied respectively, then we obtain…”

“…Using essentially the fixed point formulation and projection technique, many researchers [5][6][7][8][9][10][11] studied related iterative schemes for approximating the solutions to systems of variational inequalities. On the other hand, over the past three decades, there has been quite an activity in the development of powerful and highly efficient numerical methods to solve the VIP and its applications [12][13][14][15][16][17][18]. There is a substantial number of methods, including the linear approximation method [19,20], the auxiliary principle [21,22], the projection technique [9,11], and the descent framework [23].…”