Strong convergence for variational inequalities and equilibrium

در اين مقاله، ما يك الگوريتم معرفي ميكنيم كه دنباله توليد شده توسط اين الگوريتم به طور قوي به يك نقطه ثابت مشترك ازنگاشتھاي غير انبساطي يك نمايش ھمگراست به طوري كه اين نقطه جوابي مشترك از يك نامساوي تغيراتي و يك نامساوي تعادل نيز مي باشد.

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.