Method of successive approximations for abstract volterra equations in a banach space

We apply the method of successive approximations to abstract Volterra equations of the formx=f+a*Ax, whereA is a closed linear operator. The assumption is made that a kernela is continuous but is not necessarily of bounded variation. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 376–382, March, 1999.