On the Modulus of Continuity of Mappings Between Euclidean Spaces - Agbor, Dieudonné; Boman, Jan (MATHEMATICA SCANDINAVICA, 2013)
Let f be a function from R^p to R^q and let Λ be a finite set of pairs (θ, η) R^p × R^q. Assume that the real-valued function η, f(x) is Lipschitz continuous in the direction θ for every (θ, η) Λ. Necessary and sufficient conditions on Λ are given for this assumption to imply each of the following: (1) that f is Lipschitz continuous, and (2) that f is continuous with modulus of continuity Cε |ε|.