Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
Keyword(s):
Abstract Let 𝐾 be a nonempty closed convex subset of a real uniformly convex Banach space 𝐸 and 𝑆, 𝑇 : 𝐾 → 𝐾 two nonexpansive mappings such that 𝐹(𝑆) ∩ 𝐹(𝑇) := {𝑥 ∈ 𝐾 : 𝑆𝑥 = 𝑇𝑥 = 𝑥} ≠ ø. Suppose {𝑥𝑛} is generated iteratively by 𝑥1 ∈ 𝐾, 𝑥𝑛+1 = (1 – α 𝑛)𝑥𝑛 + α 𝑛𝑆[(1 – β 𝑛)𝑥𝑛 + β 𝑛𝑇𝑥𝑛], 𝑛 ≥ 1, where {α 𝑛}, {β 𝑛} are real sequences in [0, 1]. In this paper, we discuss the weak and strong convergence of {𝑥𝑛} to some 𝑥* ∈ 𝐹(𝑆) ∩ 𝐹(𝑇).
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