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Strong convergence theorems for asymptotically quasi-nonexpansive type mappings in convex metric spaces. (English) Zbl 1263.47080

The author studies the convergence problem of three-step iterative sequences with errors for asymptotically quasi-nonexpansive type mappings in convex metric spaces. He also provides some necessary and sufficient conditions for the convergence of the generated sequences to a fixed point of the asymptotically quasi-nonexpansive type mapping. The results presented in this paper extend and improve upon several existing results in the literature.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces
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