variational inequality over the intersection of fixed point sets of generalized demimetric mappings and zero point sets of maximalmonotone mappings

In this paper, we consider a variational inequality problem which is defined over the intersection of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of maximal monotone mappings. we propose an iterative algorithm combines the hybrid steepest descent method with the inertial technique to solve such a variational inequality problem and study the strong convergence of the sequence generated by the proposed algorithm. the results of this paper improve and extend several known results in the literature.