A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications

Gonzalo García Macias

Abstract

We present a novel result that, in a certain sense, generalizes the Arzelà-Ascoli theorem.  Our main tool will be the so called degree of nondensifiability, which is not a measure of noncompactness but canbe used as  an  alternative tool  in  certain  fixed problems where such  measures do  not  work  out.   To  justify  our  results,  we  analyze  the  existence  of continuous solutions  of certain  Volterra integral  equations defined by vector valued functions.


Keywords

Arzelà-Ascoli theorem; degree of nondensifiability; α-dense curves; measures of noncompactness; Volterra integral equations

Subject classification

46B50; 47H08; 45D05

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References

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