Stieltjes and Stieltjes-Volterra integral equations

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1974

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Abstract

Suppose S is an interval [a,b], R is a complete normed ring with identity, G is the complete normed group of quasi-continuous functions from S into R normed with the supremum norm, and H is the class of all functions from G into G to which {0,0} belongs. D. B. Hinton identified a class F of kernel functions F from S X S into R and a reversible transformation y from F onto F containing only pairs {F,M} which satisfy the Stieltjes-Volterra integral equation M(x, c) = 1 + (L) [integral c to x] dF[x,I]M[I,c] for all {x,c} in S X S ...

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