Constrained best approximation in Hilbert space .3. Applications to n-convex functions uri icon

abstract

  • This paper continues the study of best approximation in a Hilbert space X from a subset K which is the intersection of a closed convex cone C and a closed linear variety, with special emphasis on applications to the n-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 in K to any f in X can be reduced to the (generally much simpler) problem of finding best approximations to a certain perturbation of f from either the cone C or a certain subcone CF. We will show how to determine this subcone CF, give the precise condition characterizing when CF= C, and apply and strengthen these general results in the practically important case when C is the cone of n-convex functions in L2(a, b).

published proceedings

  • CONSTRUCTIVE APPROXIMATION

author list (cited authors)

  • Deutsch, F., Ubhaya, V. A., Ward, J. D., & Xu, Y. S.

citation count

  • 7

complete list of authors

  • Deutsch, F||Ubhaya, VA||Ward, JD||Xu, YS

publication date

  • January 1996