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On Volterra integral equations with weakly singular kernels in Banach spaces. (English) Zbl 0791.45006
The author considers the integral equation $$x(t)=g(t)+\int_{D(t)} A(t,s) f(s,x (s)) ds$$, $$t \in\mathbb{R}^ n$$, $$D(t)=\{s \in \mathbb{R}^ n | 0 \leq s_ i \leq t_ i\}$$, where $$A$$ is weakly singular and $$x$$ takes values in a Banach space $$E$$. Under certain additional conditions it is shown that there exists $$J=[0,j_ 1] \times\cdots \times [0,j_ n]$$ such that the set of all continuous solutions $$x:J \to E$$, considered as a subset of $$C(J,E)$$, is a compact $$R_ \delta$$.

##### MSC:
 45N05 Abstract integral equations, integral equations in abstract spaces 45G05 Singular nonlinear integral equations
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