Initial value methods in the theory of Fredholm integral equations

This paper deals with the problem of establishing the equivalence of a family of integral equations of Fredholm type with kernels that depend on a parameter and a related Cauchy system of integrodifferential equations. We also show how the Cauchy problem can be given an abstract formulation as an initial value problem in a complex Banach space.This research was supported by the University of Nevada at Las Vegas, Research Grant No. 4503.