Convergence theorems for total asymptotically nonexpansive mappings in hyperbolic spaces. (English) Zbl 1397.47024

Summary: The purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove some \(\Delta\)-convergence theorems of the iteration process for this kind of mappings in the setting of hyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature.


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
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