The Cayley-Hilbert metric and positive operators

Abstract

AbstractThe Cayley-Hilbert metric is defined for a real Banach space containing a closed cone. By restricting the domain of a particular type of positive nonlinear operator, the Banach contraction-mapping theorem is used to prove the existence of a unique fixed point of the operator with explicit upper and lower bounds. Applications to quasilinear elliptic partial differential equations and to matrix theory are considered