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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 1, 1998, pp. 23–35
DOI: 10.4171/ZAA/806

Published online: 1998-03-31

Complete Continuity of Some Nonlinear Volterra Operator in Banach Spaces

Martin Väth[1]

(1) Czech Academy of Sciences, Prague, Czech Republic

We consider continuity and compactness of the particular Volterra operator $Hx(t) = \int ^t_{t_0} K(r)x(r)dr$, where $K(t)$ is a nonlinear continuous and compact or a-Lipschitz operator in some Banach space.

Keywords: Nonlinear Volterra integral operators, compactness, condensing operators, nonlin-ear ordinary differential equations in Banach spaces, Bochner measurability

Väth Martin: Complete Continuity of Some Nonlinear Volterra Operator in Banach Spaces. Z. Anal. Anwend. 17 (1998), 23-35. doi: 10.4171/ZAA/806