Geodesic
Asymptotically differentiable functions of several variables
Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 857-871.

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We show that if a real function $F(x)$ is defined in an open convex set $Q\subset R_n$ and satisfies an asymptotic Lipschitz condition, then it must satisfy a Lipschitz condition. The result is used for investigating asymptotically differentiable functions. 
@article{MZM_1975_17_6_a3,
     author = {C. G. Slobodnik},
     title = {Asymptotically differentiable functions of several variables},
     journal = {Matemati\v{c}eskie zametki},
     pages = {857--871},
     publisher = {mathdoc},
     volume = {17},
     number = {6},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a3/}
}
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C. G. Slobodnik. Asymptotically differentiable functions of several variables. Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 857-871. http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a3/