Abstract
A study of local strong uniqueness is given. Concepts of local strong uniqueness and directional local strong uniqueness of at best, at worst, or exact rate ø are introduced. The relation of local strong uniqueness to the “conditioning” of the approximation problem and to the modulus of convexity of the underlying space are noted. Special emphasis is given to L p approximation. Of particular interest here is that a continuum of local strong uniqueness rates is possible for L p , 1 < p < 2; whereas, for 2 < p < ∞, only one of two possible local strong uniqueness rates can occur for each approximation problem.
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