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Weak and strong convergence theorems of quasi-nonexpansive mappings in a Hilbert spaces. (English) Zbl 1254.90298

The author proves the weak convergence of two quasi-nonexpansive mappings in a Hilbert space by using Moudafi’s iterative scheme. Weak convergence of a quasi-nonexpansive mapping and a nonexpansive mapping in a Hilbert space, using the same Moudafi’s iterative scheme, has been proved, as well. Finally, the author proves the strong convergence of two quasi-nonexpansive mappings, satisfying a certain condition, in a Hilbert space.

MSC:

90C48 Programming in abstract spaces
49J27 Existence theories for problems in abstract spaces
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