Beyond all doubts, the CA simulation has been based on the assumption that the reaction has finally reached to the 'extreme' equilibrium; for instance, the methanol conversion happens in a close system for a termless period, thus, the layout of the results somehow reflect an 'ideal' product distribution which may never occur in reality.
Maintaining this equilibrium, for instance, is particularly important in the tissues where the rate of DNA damage inflicted by free radicals is considerably high.
However, several authors have made efforts to get new existence results in the studies of equilibrium problems, for instance, [9 11].
Numerous problems in physics, optimization and economics can be reduced to finding a solution of the equilibrium problem (for instance, see [28]).
Subsequently, many authors studied the problem of finding a common element in the fixed point set of nonexpansive mappings, in the solution set of variational inequalities and in the solution set of equilibrium problems, for instance see [10 20].
Some methods have been proposed to solve the generalized mixed equilibrium problems, generalized equilibrium problems and equilibrium problems; see, for instance, [9 22].
Some methods have been proposed to solve the equilibrium problem and the generalized equilibrium problem; see, for instance, [5, 14 28].
Several iterative algorithms are proposed to solve the equilibrium problems and a finite family of equilibrium problems; see, for instance, [8 14].
The first problem is called weak vector equilibrium problem (see, for instance, [13, 17, 18]) and the second one is normally called strong vector equilibrium problem (see [19]).
Several iterative methods have been proposed to solve the equilibrium problem, see, for instance, [2 4].
Some methods have been proposed to solve the equilibrium problem; see, for instance, [7 11].
