Abstract
In this paper, we construct a modified Ishikawa iterative process to approximate common fixed points for two multivalued asymptotically nonexpansive mappings and prove some convergence theorems in uniformly convex hyperbolic spaces.
Highlights
Let D be a nonempty subset of a metric space (X, d)
H is known as the generalized Pompeiu-Hausdorff distance induced by d if
We say that a multivalued mapping T : D → P (D) has a fixed point x if x ∈ T x
Summary
Let D be a nonempty subset of a metric space (X, d). A mapping T : D → D is called asymptotically nonexpansive if for any x, y ∈ D, there exists a sequence {kn} with kn ≥ 1 and lim n→∞ kn =such that d(T nx, T ny) ≤ knd(x, y).Let P (D) represent the set of all nonempty subsets of D, Cl(D) denote the set all nonempty closed subsets of D and CB(D) denote the set all nonempty closed and bounded subsets of D. A mapping T : D → D is called asymptotically nonexpansive if for any x, y ∈ D, there exists a sequence {kn} with kn ≥ 1 and lim n→∞ We say that a multivalued mapping T : D → P (D) has a fixed point x if x ∈ T x.
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