In this paper, we proved a strong convergence of the viscosity approximation method in real Hilbert space H, relatively to the computation of fixed points of operators in the wide class of total asymptotically nonexpansive mappings. Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As an application, iterative method for approximation of solution of variational inequality problem was proposed.

Hilbert space, total asymptotically nonexpansive, variational inequality, viscosity approximation method, strong convergence.