Let be a nonempty bounded closed convex subset of a complete CAT(0) space . We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on is nonempty closed and convex. We also show that, under some suitable conditions, the sequence defined by , converges to a common fixed point of where they are asymptotic pointwise nonexpansive mappings on , are sequences in for all and is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.
"Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces." J. Appl. Math. 2012 (SI03) 1 - 17, 2012. https://doi.org/10.1155/2012/327434