Article

Two abstract approaches in vectorial fixed point theory

Published in: Quaestiones Mathematicae
Volume 41 , issue 2 , 2018 , pages: 173–188

DOI: 10.2989/16073606.2017.1376002

Author(s): Tiziana Cardinali Department of Mathematics and Computer Science, Italy , Radu Precup Department of Mathematics, Romania , Paola Rubbioni Department of Mathematics and Computer Science, Italy

Keywords: 47H10 , 54H25 , 47H10 , 54H25

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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.

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