Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces
Piyanan Pasom, Bancha Panyanak · Journal of Applied Mathematics · 2012
Let C be a nonempty bounded closed convex subset of a complete CAT(0) space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence defined by , converges to a common fixed point of T1, T2, …, Tm where they are asymptotic pointwise nonexpansive mappings on C, are sequences in [0,1] for all i = 1,2, …, m, and {nk} is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.