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Strong convergence of an Ishikawa-type algorithm in CAT(0) spaces. (English) Zbl 1470.65110

Summary: We study strong convergence of an Ishikawa-type algorithm of two asymptotically nonexpansive type maps to their common fixed point on a CAT(0) space. Our work provides an affirmative answer to the question of K.-K. Tan and H.-K. Xu [Proc. Am. Math. Soc. 122, No. 3, 733–739 (1994; Zbl 0820.47071)]; in particular, strong convergence of an Ishikawa-type algorithm of two asymptotically nonexpansive maps without the rate of convergence condition is obtained on a nonlinear domain.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
54H25 Fixed-point and coincidence theorems (topological aspects)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Citations:

Zbl 0820.47071
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References:

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