ON THE CONTINUITY OF A NONLINEAR INTEGRAL OPERATOR.
APL library bulletin translations series,
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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Let G and G be bounded closed regions in R superscript n let Kt,s,u and St,s,u carry G x G x R into R and satisfy the Caratheodory conditions measurable in t and s for all u, and continuous in u for almost all t,s. The author gives a majorization criterion for continuity and definition everywhere of the Urysohn operator Kxt the integral taken over G of Kt,s,xs ds.
- Theoretical Mathematics