△‐Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Luo Yi Shi, Ru Dong Chen and Yu Jing Wu

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: New △‐convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self‐mapping T of a closed convex subset C of a CAT(0) space X. Consider the iteration process {xn}, where x0 ∈ C is arbitrary and xn+1 = αnxn ⊕ (1 − αn)Tnyn or xn+1 = αnTnxn ⊕ (1 − αn)yn, yn = βnxn ⊕ (1 − βn)Tnxn for n ≥ 1, where {αn}, {βn}⊂(0,1). It is shown that under certain appropriate conditions on αn, βn, {xn} △‐converges to a fixed point of T.

Date: 2013
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https://doi.org/10.1155/2013/251705

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:251705

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