Almost affine functions
Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 435-440.

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The class of almost affine functions is investigated. A function is called almost-affine if, on any segment contained in its domain of definition (supposed convex), it is either constant or monotonic.
@article{MZM_1971_9_4_a9,
     author = {Ho\`ang Tụy},
     title = {Almost affine functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {435--440},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a9/}
}
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Hoàng Tụy. Almost affine functions. Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 435-440. http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a9/