Chebyshev Sets with Piecewise Continuous Metric Projection
Игорь Германович Царьков
Abstract
Abstract We study the properties of Chebyshev sets composed of at most countably many sets with a continuous metric projection. Local solarity is established in neighborhoods on which the metric projection is single-valued and continuous in uniformly convex spaces. As examples of applications of the results obtained, we consider generalized fractions and products, as well as ridge functions.
Topics & Concepts
MathematicsProjection (relational algebra)Chebyshev filterMetric (unit)Uniform continuityPure mathematicsRegular polygonPiecewiseMetric spaceDiscrete mathematicsMathematical analysisAlgorithmGeometryOperations managementEconomicsFixed Point Theorems AnalysisOptimization and Variational AnalysisAdvanced Banach Space Theory