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Linear integral equations of Volterra concerning Henstock integrals. (English) Zbl 1015.45001

For the integral equation \[ x(t)+\int _a^t\alpha (s)x(s)d s=f(t), t\in [a,b] \] with Banach space valued functions \(f,x\) and linear operator valued \(\alpha \) existence results are given if the integral in the equation is Henstock or Bochner. Some applications and examples are presented.

MSC:

45D05 Volterra integral equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A39 Denjoy and Perron integrals, other special integrals
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