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The differentiability of Banach space-valued functions of bounded variation

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Abstract

In this paper we consider Banach space-valued functions with the compact range. It is shown that if a Banach space-valued function \(F:[0,1] \rightarrow X\) is of bounded variation with respect to the Minkowski functional \(||.||_{F}\) associated to the closed absolutely convex hull \(C_{F}\) of \(F([0,1])\), then \(F\) is differentiable almost everywhere on \([0,1]\).

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Authors and Affiliations

  1. Mathematics Department, Science Natural Faculty, University of Elbasan, Elbasan, Albania

    Sokol Bush Kaliaj

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  1. Sokol Bush Kaliaj
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Correspondence to Sokol Bush Kaliaj.

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Communicated by G. Teschl.

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Kaliaj, S.B. The differentiability of Banach space-valued functions of bounded variation. Monatsh Math 173, 343–359 (2014). https://doi.org/10.1007/s00605-013-0536-8

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  • DOI: https://doi.org/10.1007/s00605-013-0536-8

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