
Accession Number : AD0657162
Title : ON THE CONTINUITY OF A NONLINEAR INTEGRAL OPERATOR.
Descriptive Note : APL library bulletin translations series,
Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
Personal Author(s) : Zabreiko,P. P.
Report Date : 26 MAY 1967
Pagination or Media Count : 8
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.
Descriptors : (*OPERATORS(MATHEMATICS), INTEGRALS), THEOREMS, INEQUALITIES, SEQUENCES(MATHEMATICS), CONVERGENCE, USSR
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE