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

Let Ω ⊂ ℝp, p ∈ ℕ* be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on 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 weakly Picard operators techniques, we study the iterates of the operator A: Some relevant examples are also given. [ABSTRACT FROM AUTHOR]