Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces

P. Pasom and B. Panyanak

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: 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 {xk} k=1∞ defined by xk+1=(11111-tmk)xk⊕tmkTmnky(m-1)k, y(m-1)k=(-t(m-1)k)xk⊕t(m-1)kTm-1nky(m-2)k,y(m-2)k=(-t(m-2)k)xk⊕t(m-2)kTm-2nky(m-3)k,…,y2k=(-t2k)xk⊕t2kT2nky1k,y1k=(-t1k)xk⊕t1kT1nky0k,y0k=xk, k∈ℕ, converges to a common fixed point of T1, T2, …, Tm 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.

Date: 2012
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https://doi.org/10.1155/2012/327434

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