Iterative methods for the computation of fixed points of demicontractive mappings. (English) Zbl 1191.65064
Authors’ abstract: This paper surveys some of the main convergence properties of the Mann-type iteration for the demicontractive mappings. Some variants of the Mann iteration that ensure the strong convergence, like the (CQ) algorithm and a variant for the asymptotically demicontractive mappings are also considered. The usual framework of our study is a (real) Hilbert space and only to a certain extent some particular Banach spaces. Historical aspects are pointed out and some applications for the convex feasibility problem are discussed.
Reviewer: Jiří Vaníček (Praha)
MSC:
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 46B99 | Normed linear spaces and Banach spaces; Banach lattices |
| 46C99 | Inner product spaces and their generalizations, Hilbert spaces |
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