The iterates of positive linear operators with the set of constant functions as the fixed point set

Let Ω ⊂ Rp, p ε N* be a nonempty subset and B(Ω) be the Branch lattice of all bounded real functions on a Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper,using the weekly P...

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Bibliographic Details
Published in:Carpathian Journal of Mathematics 2016-01, Vol.32 (2), p.165-172
Main Authors: Cătinaş, Teodora, Otrocol, Diana, Rus, Ioan A.
Format: Article
Language:English
Subjects:
Approximation
Conceptual lattices
Linear transformations
Mathematical constants
Mathematical functions
Mathematical lattices
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Summary:Let Ω ⊂ Rp, p ε N* be a nonempty subset and B(Ω) be the Branch lattice of all bounded real functions on a Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper,using the weekly Picard operators techniques,we study the iterates of the operator A.Some relevant examples are also given.
ISSN:1584-2851
1843-4401
DOI:10.37193/CJM.2016.02.04