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Motivated and inspired by the recent works on implicit iteration methods, we prove necessary and sufficient conditions for strong convergence of the eventually implicit iteration methods with errors to a common fixed point of a discrete family which is continuous total asymptotically nonexpansive (in brief, TAN) on q-uniformly smooth Banach spaces with a perturbed mapping F, 1&#x003C;q&#x2264;2, under some suitable control conditions of parameters. Some applications to viscosity approximation methods or to the eventually implicit algorithms with errors for a finite family of TAN self-mappings in real Banach spaces are also added

Implicit Iteration Methods with Errors for Discrete Non-Lipschitzian Families with Perturbed Mappings