Common fixed points for asymptotic pointwise nonexpansive mappings in metric and banach spaces - Pasom P. (2014)
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.