Nonlinear operations and the solution of integral equations
Author:
Jon C. Helton
Journal:
Trans. Amer. Math. Soc. 237 (1978), 373390
MSC:
Primary 45N05; Secondary 46G99, 47H99
MathSciNet review:
479379
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Abstract: The letters S, G and H denote a linearly ordered set, a normed complete Abelian group with zero element 0, and the set of functions from G to G that map 0 into 0, respectively. In addition, if and there exists an additive function from to the nonnegative numbers such that for each in , then only if exists for each in , and only if exists for each in . It is established that if, and only if, . Then, this relationship is used in the solution of integral equations of the form , where U and V are in . This research extends known results in that requirements pertaining to the additivity of U and V are weakened.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197804793793
PII:
S 00029947(1978)04793793
Keywords:
Sum integral,
product integral,
subdivisionrefinement integral,
nonlinear integral equation
Article copyright:
© Copyright 1978
American Mathematical Society
