DOI: 10.7494/opmath.2005.25.2.189 ISSN: 1232-9274

Convex compact family of polynomials and its stability

Michał Góra
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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.

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