Two abstract approaches in vectorial fixed point theory

Abstract

In this paper a fixed point theory is established for operators defined on Cartesian product spaces. Two abstract approaches are presented in terms of closure operators and of general functionals called measures of deviations from zero resembling the measures of noncompactness. In particular, we give vectorial versions to Mönch's fixed point theorems. An application is included to illustrate the theory.

Keywords: Fixed point, measure of noncompactness, vector-valued operator, positive matrix