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\(\Delta\)-convergence theorem for total asymptotically nonexpansive mapping in uniformly convex hyperbolic spaces. (English) Zbl 1330.47091

Summary: Recently, S. S. Chang et al. [Appl. Math. Comput. 219, No. 5, 2611–2617 (2012; Zbl 1308.47060)] introduced the concept of total asymptotically nonexpansive mappings which contain the asymptotically nonexpansive mappings. The purpose of the present paper is to analyze a three-step iterative scheme for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces. Meanwhile, we obtain a \(\Delta\)-convergence theorem of the three-step iterative scheme for total asymptotically nonexpansive mapping in CAT\((0)\) spaces. Our results obtained in this paper extend and improve some previously known results.

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)

Citations:

Zbl 1308.47060
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