Acta mathematica scientia, Series B >
HÖLDER CONTINUITY AND DIFFERENTIABILITY ON CONVERGING SUBSEQUENCES
Received date: 2011-07-18
Online published: 2012-01-20
It is shown that an arbitrary function from D ( Rn to Rm will become C0,α -continuous in almost every x ∈ D after restriction to a certain subset with limit point x. For n ≥ m differentiability can be obtained. Examples show the H¨older exponentn α = min{1, n/m} is optimal.
Volker Elling . HÖLDER CONTINUITY AND DIFFERENTIABILITY ON CONVERGING SUBSEQUENCES[J]. Acta mathematica scientia, Series B, 2012 , 32(1) : 75 -83 . DOI: 10.1016/S0252-9602(12)60005-8
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