ON THE CONTINUITY OF A NONLINEAR INTEGRAL OPERATOR.
Abstract
Let G and G* be bounded closed regions in R superscript n; let K(t,s,u) and S(t,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 Kx(t) = the integral taken over G of K(t,s,x(s)) ds.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 26, 1967
- Accession Number
- AD0657162
Entities
People
- P. P. Zabreiko
Organizations
- Johns Hopkins University Applied Physics Laboratory