Nonlinear operations and the solution of integral equations

Author:
Jon C. Helton

Journal:
Trans. Amer. Math. Soc. **237** (1978), 373-390

MSC:
Primary 45N05; Secondary 46G99, 47H99

MathSciNet review:
479379

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Abstract | References | Similar Articles | Additional Information

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/S0002-9947-1978-0479379-3

Keywords:
Sum integral,
product integral,
subdivision-refinement integral,
nonlinear integral equation

Article copyright:
© Copyright 1978
American Mathematical Society