Composite extragradient implicit rule for solving a hierarch variational inequality with constraints of variational inclusion and fixed point problems

Let X be a uniformly convex and q-uniformly smooth Banach space with 1<q <= 2. In the framework of this space, we are concerned with a composite gradient-like implicit rule for solving a hierarchical monotone variational inequality with the constraints of a system of monotone variational inequalities, a variational inclusion and a common fixed point problem of a countable family of nonlinear operators {Sn}n=0 infinity</mml:msubsup>. Our rule is based on the Korpelevich extragradient method, the perturbation mapping, and the W-mappings constructed by {S-n}(n=0)(infinity).