Strong convergence of a general implicit algorithm for variational inequality problems and equilibrium problems and a continuous representation of nonexpansive mappings

Lashkarizadeh Bami, M.; Soori, E.

Strong convergence of a general implicit algorithm for variational inequality problems and equilibrium problems and a continuous representation of nonexpansive mappings

Authors

M. Lashkarizadeh Bami ¹

E. Soori ²

¹ Isfahan university

² isfahan university

Abstract

We introduce a general implicit algorithm for finding a common element of‎
‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎
‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the solution of systems of equilibrium‎
‎problems and the common fixed points of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎.

Keywords

Continuous representation‎

‎invariant mean‎

‎equilibrium problem‎

‎nonexpansive mapping‎

‎classical variational inequality‎

Subjects