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The freezing method for Volterra integral equations in a Banach space. (English) Zbl 1178.45014
Summary: The “freezing” method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type
$x(t)- \int_0^t K(t, t-s)x(s)ds =f(t)\quad(t\geq 0),$
where $$K(t,s)$$ is an operator valued function “slowly” varying in the first argument. Besides, sharp explicit stability conditions are derived.

##### MSC:
 45N05 Abstract integral equations, integral equations in abstract spaces 45D05 Volterra integral equations 45M10 Stability theory for integral equations
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