Hierarchical variational inequality problem and split common fixed point of averaged operators

Abstract

In this paper, we consider a variational inequality problem which is defined over the intersection of the solution set of variational inequality problem and the solution set of split common fixed point problem for averaged operators in Hilbert spaces. We present a new and efficient iterative method for solving this problem and establish its strong convergence. The proposed algorithm does not require knowledge of the Lipschitz constants of the operators and does not depend on the prior information of the bounded linear operator norms. Finally, we apply our result to study certain classes of optimization problems, and present some numerical experiments to demonstrate the applicability of our proposed algorithm.