, Volume 18, Issue 4, pp 553-560

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

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