Accession Number : AD0742914

Title :   Local and Asymptotic Approximations of Nonlinear Operators by (k(1), ..., k(N))-Homogeneous Operators.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Moore,R. H. ; Nashed,M. Z.

Report Date : JAN 1972

Pagination or Media Count : 33

Abstract : Notions of local and asymptotic approximations of a nonlinear mapping F between normed linear spaces by a sum of N k(i)-homogeneous operators are defined and investigated. It is shown that the approximating operators inherit from F properties related to compactness and measures of noncompactness. As a byproduct, the well-known result that the Frechet (or asymptotic) derivative of a compact operator is compact is generalized in several directions and to families of operators. The notions introduced are examined within a hierarchy of other notions of local and asymptotic approximations and related differentials. Nets of equi-approximable operators with collectively compact (or bounded) approximates, which arise in approximate solutions of integral and operator equations, are studied with particular reference to pointwise (or weak convergence) properties. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, OPERATORS(MATHEMATICS)), ASYMPTOTIC SERIES, MEASURE THEORY, VECTOR SPACES, MAPPING(TRANSFORMATIONS), CONVEX SETS, THEOREMS, BANACH SPACE, INTEGRAL EQUATIONS, APPROXIMATION(MATHEMATICS), NONLINEAR SYSTEMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE