Implicit Iteration Methods with Errors for Discrete Non-Lipschitzian Families with Perturbed Mappings
© T.-H. Kim and K.-Y. Kim. 2010
Received: 31 October 2009
Accepted: 3 March 2010
Published: 25 March 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.
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