Fixed Point Theorems for Proximately Nonexpansive Semigroups
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AbstractA commutative semigroup G of continuous, selfmappings on (X, d) is called proximately nonexpansive on X if for every x in X and every (β > 0, there is a member g in G such that d(fg(x),fg(y)) ≤ (1 + β) d (x, y) for every f in G and y in X. For a uniformly convex Banach space it is shown that if G is a commutative semigroup of continuous selfmappings on X which is proximately nonexpansive, then a common fixed point exists if there is an x0 in X such that its orbit G(x0) is bounded. Furthermore, the asymptotic center of G(x0) is such a common fixed point.
1976 ◽
Vol 15
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pp. 87-96
1992 ◽
Vol 53
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pp. 25-38
1989 ◽
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pp. 113-117
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1974 ◽
Vol 80
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pp. 1123-1127
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2018 ◽
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pp. 883
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2001 ◽
Vol 26
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pp. 183-188
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1993 ◽
Vol 16
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pp. 81-86
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