Opuscula Math. 25, no. 2 (2005), 189-194
Opuscula Mathematica
Convex compact family of polynomials and its stability
Abstract. Let \(P\) be a set of real polynomials of degree \(n\). Set \(P\) can be identified with some subset \(P\) of \(\mathbb{R}^n\) consists of vectors of coefficients of \(P\). If \(P\) is a polytope, then to ascertain whether the entire family of polynomials \(P\) is stable or not, it suffices to examine the stability of the one-dimensional boundary sets of \(P\). In present paper, we extend this result to convex compact polynomial families. Examples are presented to illustrate the results.
Keywords: stability, convex set of polynomials, regular set.
Mathematics Subject Classification: 26C10, 30C15, 52A20, 65L07.
- Michał Góra
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
- Received: 2004-10-22.
