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ŁOJASIEWICZ-TYPE INEQUALITIES AND GLOBAL ERROR BOUNDS FOR NONSMOOTH DEFINABLE FUNCTIONS IN O-MINIMAL STRUCTURES
Published online by Cambridge University Press: 10 August 2015
Abstract
In this paper, we give some Łojasiewicz-type inequalities for continuous definable functions in an o-minimal structure. We also give a necessary and sufficient condition for the existence of a global error bound and the relationship between the Palais–Smale condition and this global error bound. Moreover, we give a Łojasiewicz nonsmooth gradient inequality at infinity near the fibre for continuous definable functions in an o-minimal structure.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 99 - 112
- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.