Abstract
The aim of this chapter is to introduce the class of piecewise differentiable functions and to investigate the differential properties of these functions. In particular, we show that a piecewise differentiable function is a locally Lipschitz continuous B-differentiable function and provide a condition which ensures that a piecewise differentiable function is strongly B-differentiable. Finally, we introduce the notion of a \(P{C}^{r}\)-homeomorphism and provide inverse and implicit function theorems for piecewise differentiable functions.
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© 2012 Stefan Scholtes
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Scholtes, S. (2012). Piecewise Differentiable Functions. In: Introduction to Piecewise Differentiable Equations. SpringerBriefs in Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4340-7_4
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DOI: https://doi.org/10.1007/978-1-4614-4340-7_4
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