A Lipschitz constant formula for vector addition in cones with applications to Stein-like equations
Document Type
Article
Publication Date
3-1-2012
Abstract
For a cone C equipped with the Thompson metric and A ∈ C, we show that the translation map x {mapping} x + a is a strict contraction on any lower (or initial) set C ∩ x -C of the cone and derive an explicit formula for the Lipschitz constant. We apply our results to Stein equations, Riccati equations, and Ferrante-Levy equations on normal cones of Banach spaces to establish the existence, uniqueness and continuous dependence on parameters of positive solutions. © 2011 Springer Basel AG.
Publication Source (Journal or Book title)
Positivity
First Page
81
Last Page
95
Recommended Citation
Lawson, J., & Lim, Y. (2012). A Lipschitz constant formula for vector addition in cones with applications to Stein-like equations. Positivity, 16 (1), 81-95. https://doi.org/10.1007/s11117-011-0112-1
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