Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

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.


References [Enhancements On Off] (What's this?)

  • [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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 45.30, 34.00

Retrieve articles in all journals with MSC: 45.30, 34.00


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

American Mathematical Society