Abstract
The main purpose of this paper is to study Browder type convergence theorems for a nonexpansive semigroup with geometric approaches in a CAT(κ) space. Besides, we determine a necessary and sufficient condition for convergence of a Browder type iteration associated to a uniformly asymptotically regular nonexpansive semigroup on the unit sphere in an infinite-dimensional Hilbert space. MSC:47H20, 47H10.
Highlights
Let (X, d) be a metric space, C a closed convex subset of X and T : C → C a mapping
Recall that T is nonexpansive on C if d(Tx, Ty) ≤ d(x, y), for all x, y ∈ C
In, Browder [ ] was the pioneer to consider an implicit scheme and prove the following strong convergence theorem of this algorithm in a Hilbert space
Summary
Let (X, d) be a metric space, C a closed convex subset of X and T : C → C a mapping. Recall that T is nonexpansive on C if d(Tx, Ty) ≤ d(x, y), for all x, y ∈ C. Let C be a bounded closed convex subset of a Hilbert space and T a nonexpansive mapping on C.
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