Heterogeneous vectorial fixed point theorems

Abstract

In this paper, we obtain fixed point theorems for operators defined on Cartesian product spaces under heterogeneous conditions upon the structure of the factor spaces and the operator components. The main results combine Banach–Perov contraction principle with topological fixed point theorems of Mönch type in strong and weak topologies. The results make possible a tinted analysis of the operator systems. An application of the vectorial technique to evolution equations with nonlocal Cauchy conditions is included.

Authors

Tiziana Cardinali
Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

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

Paola Rubbioni
Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

Keywords

Fixed point; vector-valued operator; measure of noncompactness; measure of weak noncompactness; evolution equation; nonlocal Cauchy condition.

Paper coordinates

T. Cardinali, R. Precup, P. Rubbioni, Heterogeneous vectorial fixed point theorems, Mediterr. J. Math., 14 (2017) art. no. 83, 12 pp., https://doi.org/10.1007/s00009-017-0888-8

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About this paper

Journal

Metditerranean Journal Mathematics

Publisher Name

Birkhauser Verlag Basel

Print ISSN
1660-5446
Online ISSN

1660-5454

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