Abstract
In this paper, using a multistep iterative scheme, we establish strong and Δ-convergence theorems for finite families of total asymptotically quasi-nonexpansive mappings in uniformly convex hyperbolic spaces. We then establish Δ- and polar convergence theorems for finite families of total asymptotically nonexpansive mappings in CAT(0) spaces. These new theorems are extensions, improvements, and generalizations of some recently announced results by many authors.
Highlights
For a closed convex and nonempty subset K of a uniformly convex metric space X and a bounded sequence {xn}, we shall write xn x if and only if φ(x) = infy∈K φ(y) where φ(y) = lim supn→∞ d(xn, y); see, for example, [ ]
Let (X, d) be a metric space, x, y ∈ X, and d(x, y) = l
A metric space (X, d) is called a geodesic space if every two points of X are joined by a geodesic segment
Summary
For a closed convex and nonempty subset K of a uniformly convex metric space X and a bounded sequence {xn}, we shall write xn x if and only if φ(x) = infy∈K φ(y) where φ(y) = lim supn→∞ d(xn, y); see, for example, [ ]. New fixed point results were studied by many authors in the setting of hyperbolic and CAT( ) metric spaces; see, for example, [ , , , – ], and the references therein. Chang et al [ ] proved strong and -convergence theorems for total asymptotically nonexpansive mappings in CAT( ) spaces.
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