The elastica can be understood from a number of different aspects, including as a mechanical equilibrium, a problem of the calculus of variations, and the solution to elliptic integrals.
Recently, a problem of finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping is studied by Takahashi and Zembayashi in [15, 16].
Vector variational inequalities have proved to be efficient tools for investigating vector optimization problems and they also provide with a mathematical model for the problems of equilibrium in a mechanical structure when there are several aspects (weight, cost, resistance etc).
The problem is a generalization of equilibrium problem proposed by Blum and Oettli [2].
This form creates problems of equilibrium that do not exist in lintels.
Then the sequence ({x_{n}}) converges strongly to (Pi_{F}x_{1}), where (Pi_{F}) is the generalized projection from E onto F. Corollary 3.3 improves the main theorem in Huang and Ma [8] from an equilibrium problem to a family of equilibrium problems.
It is well known that the vector equilibrium problem is a vital extension of equilibrium problems, which contain vector variational inequality, vector complementarity problems, and vector optimization problems as special cases.
As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems.
Our results are applied to study the approximation problem of solution to a system of equilibrium problems.
In 2000, Ansari et al. [5] introduced the system of vector equilibrium problems (SVEPs), that is, a family of equilibrium problems for vector-valued bifunctions defined on a product set, with applications in vector optimization problems and Nash equilibrium problem [11] for vector-valued functions.
In 2003, Fu [1] introduced the symmetric vector quasi-equilibrium problem (for short, SVQEP) which is a generalization of equilibrium problem proposed by Blum and Oettli [2] and gave an existence theorem for a weak Pareto solution for (SVQEP).
