A product integral solution of a Stieltjes-Volterra integral equation.
Author:
James A. Reneke
Journal:
Proc. Amer. Math. Soc. 24 (1970), 621-626
MSC:
Primary 45.30; Secondary 34.00
DOI:
https://doi.org/10.1090/S0002-9939-1970-0252999-5
MathSciNet review:
0252999
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Abstract | References | Similar Articles | Additional Information
Abstract: This paper demonstrates that the theory of Stieltjes-Volterra integral equations may be subsumed in Mac Nerney’s general integral equation theory by making suitable choices of linear spaces and sets of operators.
- D. B. Hinton, A Stieltjes-Volterra integral equation theory, Canadian J. Math. 18 (1966), 314–331. MR 188733, DOI https://doi.org/10.4153/CJM-1966-035-3
- Ralph E. Lane, The integral of a function with respect to a function, Proc. Amer. Math. Soc. 5 (1954), 59–66. MR 59346, DOI https://doi.org/10.1090/S0002-9939-1954-0059346-3
- J. S. MacNerney, Integral equations and semigroups, Illinois J. Math. 7 (1963), 148–173. MR 144179
- J. S. MacNerney, A nonlinear integral operation, Illinois J. Math. 8 (1964), 621–638. MR 167815
- J. W. Neuberger, Continuous products and nonlinear integral equations, Pacific J. Math. 8 (1958), 529–549. MR 102723
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Keywords:
Product integral,
Stieltjes-Volterra integral equations,
left integral,
right integral,
order additive functions,
order multiplicative functions
Article copyright:
© Copyright 1970
American Mathematical Society