Strong convergence for variational inequalities and equilibrium problems and representations

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

E. Soori ¹

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

تاریخ دریافت : 1392/08/13 تاریخ پذیرش : 1392/08/13 تاریخ انتشار : 1392/09/10

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

چکیده مقاله :

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.