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|Paper IPM / M / 520||
Let X be a reflexive Banach space and (xn)n ≥ 0 a nonexpansive
(resp., firmly nonexpansive) sequence in X.
It is shown that the set of weak ω-limit points of the
sequence (xn/n)n ≥ 1 (resp., (xn+1−xn)n ≥ 0) always
lies on a convex subset of a sphere centered at the origin of radius
d=limn→ ∞|| xn/n||. This fact quickly yields
previous results of B. Djafari Rouhani as well as recent results of
J.S. Jung and J.S. Park. Potential applications are also discussed.
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