The equivalence between the convergence of modified Picard, modified Mann, and modified Ishikawa iterations
The authors consider equivalence between the convergence for the modified Picard iteration, the modified Mann iteration, and the modified Ishikawa iteration. All those modified iterations are for \(L\)-Lipschitz mappings, Banach contractive mappings, nonexpansive mappings, and asymptotically nonexpansive mappings in Banach spaces. Some conditions related to positive series are proved to be sufficient for the mentioned equivalence.
scientific article; zbMATH DE number 2082773