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Linear Volterra Integral Equations

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Abstract

The Kurzweil-Henstock integral formalism is applied to establish the existence of solutions to the linear integral equations of Volterra-type

$$ x{\left( t \right)} + \;{}^{ * }{\int_{{\left[ {a,t} \right]}} {\alpha {\left( s \right)}x{\left( s \right)}ds = f{\left( t \right)}} },\;t \in {\left[ {a,b} \right]}, $$
(1)

where the functions are Banach-space valued. Special theorems on existence of solutions concerning the Lebesgue integral setting are obtained. These sharpen earlier results.

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Authors and Affiliations

  1. Department of Mathematics, University of São Paulo, CP 668, 13560-970 SP, São Paulo, Brazil

    M. Federson

  2. Department of Mathematics, University of São Paulo, CP 66281, 05315-970 SP, São Paulo, Brazil

    R. Bianconi & L. Barbanti

Authors
  1. M. Federson
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  2. R. Bianconi
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  3. L. Barbanti
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Correspondence to M. Federson.

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Federson, M., Bianconi, R. & Barbanti, L. Linear Volterra Integral Equations. Acta Mathematicae Applicatae Sinica, English Series 18, 553–560 (2002). https://doi.org/10.1007/s102550200057

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  • DOI: https://doi.org/10.1007/s102550200057

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