On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems

摘要

Our aim is introduce a new class of procedures, the Uniformly Asymptotically Regular-class of procedures (UAR-precedures). Then by a UAR-procedure we prove the convergence of two explicit iterative methods to the unique solution of a variational inequality problem on the set of common fixed points of a family of mappings, in the setting of Hilbert spaces.