IMPLICIT AND EXPLICIT ALGORITHMS FOR A SYSTEM OF NONLINEAR VARIATIONAL INEQUALITIES IN BANACH SPACES

摘要

In this paper, we consider a general system of nonlinear variational inequalities (in short, GSVI) in the setting of Banach spaces. We first establish the equivalence between GSVI and a system of fixed point problems. By utilizing this equivalence, we construct an implicit algorithm of Mann's type for solving GSNVI. We also propose another explicit algorithm of Mann's type for solving GSNVI. Finally, under very mild conditions, we prove the strong convergence of the sequences generated by the proposed algorithms.