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Full-Text Articles in Physical Sciences and Mathematics
Continuities Of Metric Projection And Geometric Consequences, Robert Huotari, Wu Li
Continuities Of Metric Projection And Geometric Consequences, Robert Huotari, Wu Li
Mathematics & Statistics Faculty Publications
We discuss the geometric characterization of a subset K of a normed linear space via continuity conditions on the metricprojection onto K. The geometric properties considered includeconvexity, tubularity, and polyhedral structure. The continuityconditions utilized include semicontinuity, generalized stronguniqueness and the non-triviality of the derived mapping. Infinite-dimensional space with the uniform norm we show thatconvexity is equivalent to rotation-invariant almost convexityand we characterize those sets every rotation of which has continuousmetric projection. We show that polyhedral structure underliesgeneralized strong uniqueness of the metric projection.
Best Quasi-Convex Uniform Approximation, S. E. Weinstein, Yuesheng Xu
Best Quasi-Convex Uniform Approximation, S. E. Weinstein, Yuesheng Xu
Mathematics & Statistics Faculty Publications
No abstract provided.