Geodesic
On Fixed and Periodic Points Under Certain Sets of Mappings
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 813-822

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Let (X, d) be a metric space and f a mapping of X into itself. D.F. Bailey [l] considered a class of mappings f satisfying the condition: ∀x, y ∈ X, x ≠ y, (1.1) where I+ denotes the set of positive integers. 
Holmes, R.D. On Fixed and Periodic Points Under Certain Sets of Mappings. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 813-822. doi: 10.4153/CMB-1969-106-1
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     author = {Holmes, R.D.},
     title = {On {Fixed} and {Periodic} {Points} {Under} {Certain} {Sets} of {Mappings}},
     journal = {Canadian mathematical bulletin},
     pages = {813--822},
     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-106-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-106-1/}
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