Approximating fixed points of nonexpansive mappings and solving systems of variational inequalities

‎A new approximation method for the set of common fixed points of‎ ‎nonexpansive mappings and the set of solutions of system s of‎ ‎variational inequalities is introduced and studied‎. ‎Moreover‎, ‎we‎ ‎apply our main result to obtain strong convergence theorem to a‎ ‎common fixed point of a nonexpannsive mapping and solutions of ‎ a ‎system of variational inequalities of an inverse strongly monotone‎ ‎mapping and strictly pseudo-contractive mapping of‎ ‎Browder-Petryshyn type‎.