A general composite steepest-descent method for hierarchical fixed point problems of strictly pseudocontractive mappings in Hilbert spaces

In this paper, we propose general composite implicit and explicit steepest-descent schemes for hierarchical fixed point problems of strictly pseudocontractive mappings in a real Hilbert space. These composite steepest-descent schemes are based on the well-known viscosity approximation method, hybrid steepestdescent method and strongly positive bounded linear operator approach. We obtain some strong convergence theorems under suitable conditions. Our results supplement and develop the corresponding ones announced by some authors recently in this area.