Vol. 60, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
Nonlinear integral equations and product integrals

Alvin John Kay

Vol. 60 (1975), No. 1, 203–222

B. W. Helton has studied linear equations of the form

f (x) = f(a)+ (RL ) x (Kf + M f );

this paper extends some of his results to a nonlinear setting. Let S be a linearly ordered set, {G,+, ∥} a complete normed abelian group, H the set of functions from G to G that take 0 to 0, 𝒪𝒜 and 𝒪ℳ classes of functions from SXS to H that are order-additive and order-multiplicative respectively and satisfy a Lipschitz-type condition, and be J. S. Mac Nerney’s reversible mapping from 𝒪𝒜 onto 𝒪ℳ. If {V,W} is in , we show the collection of all functions that are differentially equivalent to V is the same as the collection of functions that are differentially equivalent to W 1. This analysis is used to prove existence theorems for product integrals which we show solve (1).

Received: 29 May 1974
Revised: 9 September 1974
Published: 1 September 1975
Alvin John Kay