Geodesic
On Asymptotically Nonexpansive Semigroups of Mappings
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 209-214

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A selfmapping f of a metric space (X, d) is nonexpansive (ε-nonexpansive) if d(f(x), f(y)) ≤ d(x, y) for all x, y ∊ X (respectively if d(x, y) < ε). In [1], M. Edelstein proved that a nonexpansive mapping f of En admits a fixed point provided the f-closure of En (i.e. the set of all points which are cluster points of {fn (x)} for some x) is nonempty. R. D. Holmes [2] considered commutative semigroups of selfmappings of a metric space and obtained fixed point theorems for such semigroups under certain contractivity conditions. 
Holmes, R. D.; Narayanaswami, P. P. On Asymptotically Nonexpansive Semigroups of Mappings. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 209-214. doi: 10.4153/CMB-1970-042-1
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     author = {Holmes, R. D. and Narayanaswami, P. P.},
     title = {On {Asymptotically} {Nonexpansive} {Semigroups} of {Mappings}},
     journal = {Canadian mathematical bulletin},
     pages = {209--214},
     year = {1970},
     volume = {13},
     number = {2},
     doi = {10.4153/CMB-1970-042-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-042-1/}
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