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.

**[1]**D. B. Hinton,*A Stieltjes-Volterra integral equation theory*, Canad. J. Math.**18**(1966), 314-331. MR**32**#6169. MR**0188733 (32:6169)****[2]**R. E. Lane,*The integral of a function with respect to a function*, Proc. Amer. Math. Soc.**5**(1954), 59-66. MR**15**, 514. MR**0059346 (15:514e)****[3]**J. S. Mac Nerney,*Integral equations and semigroups*, Illinois J. Math.**7**(1963), 148-173. MR**26**#1726. MR**0144179 (26:1726)****[4]**-,*A nonlinear integral operation*, Illinois J. Math.**8**(1964), 621-638. MR**29**#5082. MR**0167815 (29:5082)****[5]**J. W. Neuberger,*Continuous products and nonlinear integral equations*, Pacific J. Math.**8**(1958), 529-549. MR**21**#1509. MR**0102723 (21:1509)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1970-0252999-5

Keywords:
Product integral,
Stieltjes-Volterra integral equations,
left integral,
right integral,
order additive functions,
order multiplicative functions

Article copyright:
© Copyright 1970
American Mathematical Society