Complete Continuity of Some Nonlinear Volterra Operator in Banach Spaces

Abstract

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