The Stability of Dynamical System for the Quasi Mixed Equilibrium Problem in Hilbert Spaces

Narin Petrot, Jittiporn Tangkhawiwetkul

Abstract

In this paper, we study the quasi mixed equilibrium problem in Hilbert spaces and consider the existence solution of such problem. The resolvent equation which is equivalent to the quasi mixed equilibrium problem is presented and the relation between the solution of the quasi mixed equilibrium problem and such equation is proposed. Using the previous relation, we can introduce a dynamical system associated with the quasi mixed equilibrium problem. Finally, the existence and stability of such dynamical system are proved.