On the Modulus of Continuity of Mappings Between Euclidean Spaces
DOI:
https://doi.org/10.7146/math.scand.a-15238Abstract
Let f be a function from Rp to Rq and let Λ be a finite set of pairs (θ,η)∈Rp×Rq. 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|logϵ|.Downloads
Published
2013-03-01
How to Cite
Agbor, D., & Boman, J. (2013). On the Modulus of Continuity of Mappings Between Euclidean Spaces. MATHEMATICA SCANDINAVICA, 112(1), 147–160. https://doi.org/10.7146/math.scand.a-15238
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