The role of matrices that are convergent to zero in the study of semilinear operator systems

Abstract

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.

Authors

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Semilinear operator system; Vector-valued norm; Matrix convergent to zero; Fixed point; Krasnoselskii cone fixed point theorem

Paper coordinates

R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Math. Comp. Modelling 49 (2009), 703-708, https://doi.org/10.1016/j.mcm.2008.04.006

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About this paper

Journal

Mathematical and Computer Modelling

Publisher Name

Elsevier

Print ISSN
Online ISSN

0895-7177

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