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

## Abstract

Let Omega subset of R-p, p is an element of N* 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 of B(Omega) be a linear sublattice of B(Omega) and A: X -&gt; 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.

## Authors

T. Catinas
(Babes Bolyai Univ.)

D. Otrocol
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

I.A. Rus
(Babes Bolyai Univ.)

## Keywords

Banach lattice; iterates of an operator; linear operator; linear and positive operator; linear fixed point partition; fixed point; weakly Picard operator

## Cite this paper as:

T. Catinas, D. Otrocol, I.A. Rus, The iterates of positive linear operators with the set of constant functions as the fixed point set, Carpathian J. Math., Vol. 32(2016) no. 2, pp. 165-172.

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##### Journal

Carpathian Journal of Mathematics

##### Publisher Name

North Univ. Baia Mare, Romania

1584-2851

1843-4401

MR3587884