ISSN:
1432-0940
Keywords:
Primary
;
41A65
;
Secondary
;
41A29
;
Best constrained approximation
;
Shape-preserving interpolation
;
Cones
;
Dual cones
;
Duality
;
n-Convex functions
;
Hilbert space
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper continues the study of best approximation in a Hilbert spaceX from a subsetK which is the intersection of a closed convex coneC and a closed linear variety, with special emphasis on application to then-convex functions. A subtle separation theorem is utilized to significantly extend the results in [4] and to obtain new results even for the “classical” cone of nonnegative functions. It was shown in [4] that finding best approximations inK to anyf inX can be reduced to the (generally much simpler) problem of finding best approximations to a certain perturbation off from either the coneC or a certain subconeC F. We will show how to determine this subconeC F, give the precise condition characterizing whenC F=C, and apply and strengthen these general results in the practically important case whenC is the cone ofn-convex functions inL 2 (a,b),
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02433049
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