Iterative methods for hierarchical common fixed point problems and variational inequalities

The purpose of this paper is to deal with the problem of finding hierarchically a common fixed point of a sequence of nearly nonexpansive self-mappings defined on a closed convex subset of a real Hilbert space which is also a solution of some particular variational inequality problem. We introduce two explicit iterative schemes and establish strong convergence results for sequences generated iteratively by the explicit schemes under suitable conditions. Our strong convergence results include the previous results as special cases, and can be viewed as an improvement and refinement of several corresponding known results for hierarchical variational inequality problems. ©#CPRSahu et al.; licensee Springer.