Extending n-convex functions

• Autorzy: Allan Pinkus , Dan Wulbert
• Języki publikacji: EN

Abstrakty

EN

We are given data α₁,..., αₘ and a set of points E = {x₁,...,xₘ}. We address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions $f(x_{i}) = α_{i}$, i = 1,...,m, that is also n-convex on a set properly containing E. We consider both one-point extensions of E, and extensions to all of ℝ. We also determine bounds on the n-convex functions satisfying the above interpolation conditions.

Kategorie tematyczne

• 26A51: Convexity, generalizations
• 41A05: Interpolation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 171
• Numer: 2
• Strony: 125-152

Daty

wydano

2005

Twórcy

autor

Allan Pinkus

• Department of Mathematics, Technion, 32000 Haifa, Israel

autor

Dan Wulbert

• Department of Mathematics, University of California, San Diego (UCSD), 9500 Gilman Drive, La Jolla, CA 92093-0112, U.S.A.

Identyfikatory

DOI

10.4064/sm171-2-2