The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space

In this paper, using a new nonlinear mapping called demimetric and the shrinking projection method, we prove a strong convergence theorem for finding a common element of the set of common fixed points for a finite family of these new demimetric mappings and the set of common solutions of variational inequality problems for a finite family of inverse strongly monotone mappings in a Hilbert space. Using the result, we obtain well-known and new strong convergence theorems in a Hilbert space.