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Convergence theorems for total asymptotically nonexpansive mappings.

In this paper, a demiclosed principle for total asymptotically nonexpansive mappings is established. An implicit iterative method for the class of total asymptotically nonexpansive mappings is considered. Weak and strong convergence theorems are established in a real Hilbert space. As applications of main results, an equilibrium problem is considered based on implicit iterative process.