Almost stability of the Mann type iteration method with error term involving strictly hemicontractive mappings in smooth Banach spaces
1 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
2 Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan
3 Faculty of Mechanical Engineering, University of Belgrade, Al. Rudara 12-35, Belgrade, 11 070, Serbia
Journal of Inequalities and Applications 2012, 2012:207 doi:10.1186/1029-242X-2012-207Published: 24 September 2012
Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and 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.