The role of matrices that are convergent to zero in the study of semilinear operator systems
In this paper we explain the advantage of vector-valued norms and the role of matrices that are convergent to zero in the study of semilinear operator systems by means of some basic methods of nonlinear analysis: the contraction principle, Schauder's fixed point theorem, the Leray-Schauder continuation principle and Krasnoselskii's cone fixed point theorem. A vector version of Krasnoselskii's theorem is also established. (c) 2008 Elsevier Ltd. All rights reserved.
vector-valued norm fixed point matrix convergent to zero krasnoselskii cone fixed point theorem