Title
The exponent of Hlder calmness for polynomial systems: Connections between polynomial degree and exponent of Hlder calmness,Used
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This work is concerned with an analysis of Hlder calmness, a stability property derived from the concept of calmness. On the basis of characterizations for sublevel sets, procedures to determine points in such sets under a Hlder calmness assumption are analyzed. Also sufficient conditions for Hlder calmness of sublevel sets and of inequality systems will be given and examined. Further, since Hlder calmness of nonempty solution sets of finite inequality systems may be described in terms of error bounds, the local propositions are amplified to global ones. As an application the case of sublevel sets of polynomials and of general solution sets of polynomial systems is investigated. The question to be answered is in which way the maximal degree of the involved polynomials is connected to the exponent of Hlder calmness or of the error bound for the system in question.
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