Acta Mathematicae Applicatae Sinica

, Volume 18, Issue 4, pp 553–560

Linear Volterra Integral Equations

Original Papers

DOI: 10.1007/s102550200057

Cite this article as:
Federson, M., Bianconi, R. & Barbanti, L. Acta Mathematicae Applicatae Sinica, English Series (2002) 18: 553. doi:10.1007/s102550200057

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.

Keywords

Linear Volterra integral equations Kurzweil-Henstock integrals 

2000 MR Subject Classification

45A05 26A39 28B05 

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of São PauloSão PauloBrazil
  2. 2.Department of MathematicsUniversity of São PauloSão PauloBrazil

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