Implicit Iteration Methods with Errors for Discrete Non-Lipschitzian Families with Perturbed Mappings
Tae-Hwa Kim, Kui-Yeon Kim · Journal of Inequalities and Applications · 2010
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 -uniformly smooth Banach spaces with a perturbed mapping , , 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.