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Suppose f, h and G are functions with values in a normed complete ring. With suitable restrictions on these functions, it is established that f(x) = h(x) + fax f(u)G(u, v) for a 0, then there exists a subdivision D of [a, b] such that, if Ix_In_ is a refinement of D, then IL X'n1 GI < E. Further, G E OA' on [a, b] only if fab G exists and fab G fGI = 0. The statement that ajIb (1 + G) exists means there exists an element L Presented to the Society, March 4, 1974; received by the editors January 17, 1974. AMS (MOS) subject classifications (1970). Primary 45N05; Secondary 26A39, 26A42.

Solution of integral equations by product integration