Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities

In this paper, we introduce and analyze a hybrid steepest-descent viscosity algorithm for solving the triple hierarchical variational inequality problem with constraints of two problems: one generalized mixed equilibrium problem and another bilevel variational inequality problem in a real Hilbert space. Under mild conditions, the strong convergence of the iteration sequences generated by the algorithm is established. Our results improve and extend the corresponding results in the earlier and recent literature.