The fredholm and volterra problems for stieltjies integral equations

Abstract

The primary purpose of this paper is to study solutions to the integral equations, — denotes either the left Cauchy or Young integral, and g is quasi-continuous on [a, b]. Necessary and sufficient conditions for K to generate a compact operator on the quasi-continuous functions in each of these cases are given, and necessary and sufficient conditions for λ to be a regular value for the integral operators are given in the case that the operators are compact. The problem of approximating solutions to the integral equations is considered. These results are obtained as special cases of solutions to a type of abstract integral equation on an abstract function space