Strong convergence theorems of modified Halpern-Mann-type iterations for quasi-\(\phi\)-asymptotically nonexpansive mappings and applications. (Chinese. English summary) Zbl 1324.47121
Summary: The purpose of this article is to modify the Halpern-Mann-type iteration algorithm for quasi-\(\phi\)-asymptotically nonexpansive mappings to have the strong convergence under a limit condition in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results of others.
MSC:
47J25 | Iterative procedures involving nonlinear operators |
47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
47J05 | Equations involving nonlinear operators (general) |