Geodesic
Fixed Point Theorems for Proximately Nonexpansive Semigroups
Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 160-166

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DOI

A 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.
DOI : 10.4153/CMB-1986-027-2
Mots-clés : 47H10, Common fixed point, proximately nonexpansive, asymptotic center 
Kiang, Mo Tak; Tan, Kok-Keong. Fixed Point Theorems for Proximately Nonexpansive Semigroups. Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 160-166. doi: 10.4153/CMB-1986-027-2
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     title = {Fixed {Point} {Theorems} for {Proximately} {Nonexpansive} {Semigroups}},
     journal = {Canadian mathematical bulletin},
     pages = {160--166},
     year = {1986},
     volume = {29},
     number = {2},
     doi = {10.4153/CMB-1986-027-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-027-2/}
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