Almost stability of the Mann type iteration method with error term involving strictly hemicontractive mappings in smooth Banach spaces
Nawab Hussain, Arif Rafiq, Ljubomir B. Ćirić, Saleh Abdullah Al-Mezel · Journal of Inequalities and Applications · 2012
Abstract Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : K → K be a continuous strictly hemicontractive mapping. Under some conditions, we obtain that the Mann iteration method with error term converges strongly to a unique fixed point of T and is almost T-stable on K. As an application of our results, we establish strong convergence of a multi-step iteration process.