Łojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures

Abstract

In this paper, we give some Łojasiewicz-type inequalities and a nonsmooth slope inequality on non-compact domains for continuous definable functions in an o-minimal structure. We also give a necessary and sufficicent condition for which global error bound exists. Moreover, we point out the relationship between the Palais-Smale condition and this global error bound.

14 pages

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