Common fixed points for asymptotic pointwise nonexpansive mappings in metric and banach spaces

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 {x k} ∞ k=1 defined by x k+1 = (1 - t mk)x k ⊕ t mkt nk my (m-1)k,y (m-1)k = (1 - t (m-1)k)x k ⊕ t (m-1)kt nk m-1y (m-2)k,y (m-2)k = (1 - t (m-2)k)x k ⊕ t (m-2)kt nk m-2y (m-3)k,⋯,y2k = (1 - t 2k)x k ⊕ t 2kt nk 2y1k,y1k = (1 - t 1k)x k ⊕ t 1kt nk 1 y0k,y0k = x k,k ∈ ℕ,converges to a common fixed point of t 1,t 2,⋯,t m where they are asymptotic pointwise nonexpansive mappings on c,{tik} ∞ k=1 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. copyright © 2012 p. pasom and b. panyanak.