English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a CAT(0) space X. Suppose that the set Fix (T) of fixed points of T is nonempty. For a contraction f on C and t ∈ (0,1), let x t ∈ C be the unique fixed point of the contraction x → tf (x) ⊕(1 - t) T x. We will show that if X is a CAT(0) space satisfying some property, then {x t} converge strongly to a fixed point of T which solves some variational inequality. Consider also the iteration process {x n}, where x 0 ∈ C is arbitrary and x n+1 = α nf (x n) ⊕ (1-α n)Tx n for n ≥ 1, where {α n} ⊂ (0,1). It is shown that under certain appropriate conditions on α n, {x n} converge strongly to a fixed point of T which solves some variational inequality. Copyright © 2012 Luo Yi Shi and Ru Dong Chen.

Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces