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.

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In this article, we consider an iterative scheme to approximate a common fixed point for a finite family of asymptotic pointwise nonexpansive mappings. We obtain weak and strong convergence theorems of the proposed iteration in uniformly convex Banach spaces. The related results for complete CAT(0) spaces are also included. MSC: 47H09; 47H10

In this paper, we obtain the demiclosed principle, fixed point theorems, and -convergence theorems for the class of generalized hybrid mappings on CAT(κ) spaces with κ > 0. Our results extend the results of Lin et al. (Fixed Point Theory Appl. 2011:49, 2011) and many others.