Heterogeneous vectorial fixed point theorems


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.


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


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

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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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Metditerranean Journal Mathematics

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Birkhauser Verlag Basel

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