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Linear Fredholm integral equations and the integral of Kurzweil. (English) Zbl 1043.45010
Fredholm integral equations of the second kind of vector-valued functions (in Banach spaces) with Kurzweil or Henstock integrals are considered. A Fredholm alternative is proved and a corresponding ‘adjoint’ equation is obtained. The results are applied for boundary value problems on intervals.

MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
34B05 Linear boundary value problems for ordinary differential equations
45B05 Fredholm integral equations
26A39 Denjoy and Perron integrals, other special integrals
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