Strong convergence for variational inequalities and equilibrium problems and representations

Subject Areas : International Journal of Industrial Mathematics

E. Soori ¹

1 - Department of Mathematics, University of Isfahan, Isfahan, Iran.

Received: 2013-11-04 Accepted : 2013-11-04 Published : 2013-12-01

Keywords: representation, Equilibrium problem, fixed point, Nonexpansive mapping, Variational&#x0D, &#x0D, inequality,

Abstract :

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for a minimization problem and is also a common xed point for a sequence of nonexpansive mappings and a representation of nonexpansive mappings.