L et X be a compact, convex subset of a Banach space E and CC (X ) be the co l2
lection of all non2emp ty compact, coonvex subset of X equipped w ith the H ausdo rff
m etric h. Suppo se ϑis a compact, convex subset of CC (X ) and T : (ϑ, h) (ϑ, h) is
a nonexpansive m app ing. T hen fo r anyA 0 ∈ϑ, the sequence {A n } defined byA n+ 1 =
(A n + TA n )ö2 converges to a fixed po int of T. T he special case that ϑconsists of sin2
gletons only yields results p reviously obtained by H. Schaefer, M. Edelstein and S.
Ish ikaw a respectively
關聯:
Chinese Annals of Mathematics Series B 18(B4), pp.423-428