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

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

Category: Vol 32/2016 no. 2 Tags: Weakly Picard operator, Linear operator, Fixed point, Banach lattice, Iterates of an operator, Linear and positive operator, Linear fixed point partition

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Description

Let $\Omega\subset\mathbb{R}^{p},$ $p\in\mathbb{N}^{\ast}$ be a nonempty subset and $B(\Omega)$ be the Banach lattice of all bounded real functions on $\Omega$ , equipped with $sup\ norm$ . Let $X\subset B(\Omega)$ be a linear sublattice of $B(\Omega)$ and $A\colon X\rightarrow X$ be a positive linear operator
with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator $A$ . Some relevant examples are also given.

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Author(s)	Cătinaș, Teodora, Otrocol, Diana, Rus, Ioan A.