Strong convergence of the Mann iteration for alpha-demicontractive mappings

The paper deals with strong convergence properties of the Mann iteration. A new class of demicontractive mappings (called alpha-demicontractive) is introduced for which the strong convergence of the computed sequence is assured. The paper presents also an overview of relevant contributions of the last two decades, concerning strong convergence for Mann-type iteration of demicontractive mappings. (C) 2011 Elsevier Ltd. All rights reserved.