A note on the convergence of Mann iteration

DOI: https://doi.org/10.37193/CMI.2017.01.11

The main result in this note slightly generalizes Theorem 3.4 in [St. Mărușter and I. A. Rus, Kannan contractions and strongly demicontractive mappings, Creat. Math. Inform., 24 (2015), No. 3, 171–180]. We also significantly improve its proof. Both results in the paper are based on the concepts of demicontractivity and quasi-expansivity and involve relatively weak conditions that guarantee the convergence of Krasnoselskij method (the same conditions are not sufficient for the convergence of Picard iteration)