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1999/2000 Linear Integral Equations of Volterra Concerning Henstock Integrals
R. Bianconi, M. Federson
Real Anal. Exchange 25(1): 389-418 (1999/2000).

Abstract

We establish conditions for the existence of solutions of the linear integral equation of Volterra \begin{equation} x\left( t\right) +^{\ast }\int\nolimits_{[ a,t] }\alpha ( s) x ( s )\, ds=f ( t ) ,\quad t\in [ a,b ] ,\tag{$V_{\ast}$} \end{equation} where the functions are Banach space-valued and $^{\ast }\int $ denotes either the Bochner-Lebesgue or the Henstock integral. In some cases it is possible to calculate the solution of $( V)_{\ast }$ explicitly. We give several examples.

Citation

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R. Bianconi. M. Federson. "Linear Integral Equations of Volterra Concerning Henstock Integrals." Real Anal. Exchange 25 (1) 389 - 418, 1999/2000.

Information

Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 1015.45001
MathSciNet: MR1758896

Subjects:
Primary: 26A39 , 34A12 , 45D05

Keywords: Bochner integral , Henstock integral , integral equation , Volterra

Rights: Copyright © 1999 Michigan State University Press

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