Nonexpansive iterations in hyperbolic spaces

S-Iteration Process for Asymptotic Pointwise Nonexpansive Mappings in Complete Hyperbolic Metric Spaces

“…(6) Substituting (6) in to (5), we obtain Hence we get lim n→∞ d(x n , T x n ) = 0. On the other hand, we see that…”

Fixed point approximation of Picard normal S-iteration process for generalized nonexpansive mappings in hyperbolic spaces

“…This class of metric spaces in [15] covers all normed linear spaces, R-trees in the sense of Tits, the Hilbert ball with the hyperbolic metric (see [6]), Cartesian products of Hilbert balls, Hadamard manifolds (see [20]), and CAT(0) spaces in the sense of Gromov (see [4]). A thorough discussion of hyperbolic spaces and a detailed treatment of examples can be found in [15] (see also [5,6,20]). If x; y 2 X and k 2 ½0; 1; then we use the notation ð1 À kÞx È ky for Wðx; y; kÞ.…”

The fixed point property and unbounded sets in CAT(0) spaces

“…A geodesic space (X, d) is Busemann convex (firstly introduced in [3] but also known by other authors as hyperbolic metric spaces [28]) if given any pair of geodesic paths c 1 :…”