Opuscula Math. 25, no. 2 (2005), 189-194

Opuscula Mathematica

# Convex compact family of polynomials and its stability

Michał Góra

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.

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• Michał Góra
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland