We extend, using an elementary method, results of Banach (1924), Fan (1952), and Sanders (1961), which concern a finite collection of mappings with which is decomposable as , where for all and . Our theorem determines when such a collection is decomposable. We also show that such a set is unique up to an addition of a certain set, which was conjectured by Sanders.
"On the Banach mapping theorem and a related conjecture." Rocky Mountain J. Math. 52 (1) 183 - 187, February 2022. https://doi.org/10.1216/rmj.2022.52.183