Title

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

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