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