The existence of shape-preserving operators with a given action

DOI10.1216/rmjm/1181071742zbMath0932.47029OpenAlexW2025100399MaRDI QIDQ1293500

Bruce L. Chalmers, Michael Prophet

Publication date: 14 September 1999

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/RMJ28-3/cont28-3/cont28-3.html

zbMATH Keywords

monotonicityconvexitypositivityprojectiondual spaceactionbipolar theoremsimplicial coneinvariant coneshape-preserving operators

Mathematics Subject Classification ID

Linear operators on ordered spaces (47B60) Approximation by polynomials (41A10) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items (7)

Codimension-one minimal projections onto Haar subspaces ⋮ Simplicial cones and the existence of shape-preserving cyclic operators. ⋮ A note on the existence of shape-preserving projections ⋮ Minimal Multi-Convex Projections Onto Subspaces of Incomplete Algebraic Polynomials ⋮ On \(j\)-convex preserving interpolation operators ⋮ Optimal interpolating spaces preserving shape ⋮ Minimal Shape-Preserving Projections Onto Π _n : Generalizations and Extensions

Cites Work

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• Convex polynomial and spline approximation in \(C[-1,1\)]
• Shape-preserving approximation in \(L_ p\)
• The geometry of minimal shape-preserving projections onto \(\Pi_ n\)
• Degree of approximation by monotone polynomials. I
• Characterizing Shape Preserving L 1 -Approximation
• Shape-preserving polynomial approximation in C[– 1, 1]
• Monotone Approximation by Polynomials
• Minimal shape-preserving projections onto Π_n

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