Demiclosed Principle for Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Abstract

We prove the demiclosed principle for asymptotically nonexpansive mappings in CAT 0 spaces. As a consequence, we obtain a Δ-convergence theorem of the Krasnosel'skii-Mann iteration for asymptotically nonexpansive mappings in this setting. Our results extend and improve many results in the literature.

Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces

“…The result improves and extends that of Nanjaras and Panyanak [19] whose related research involves just a single mapping and the weaker ∆-convergence.…”

“…In 2010, Nanjaras and Panyanak [19] proved the demiclosed principle for asymptotically nonexpansive mappings in CAT (0) spaces. As a consequence, they also obtained a ∆-convergence theorem of the Krasnoselski-Mann iteration for asymptotically nonexpansive mappings in this setting.…”

On the strong and $\Delta$-convergence theorems for total asymptotically nonexpansive mappings on CAT(0) space

“…Nanjaras and Panyanak [13] proved the demiclosedness principle for asymptotically nonexpansive mappings and gave the ∆-convergence theorem of the modified Mann iteration process for mappings of this type in a CAT(0) space. Recently, Chang et.…”

A new iterative scheme in CAT(0) spaces with convergence analysis

“…Nanjaras and Panyanak [25] established the following relation between ∆-convergence and weak convergence in a CAT(0) space.…”