Hensel’s lemma for general continuous functions

In the present paper, we generalize the well-known Hensel’s lifting lemma to any continuous function f:Zp→Zp. This answers a question posed by Axelsson and Khrennikov (2016) who showed the validity of Hensel’s lemma for 1- and for pα-Lipschitz functions. For the statement and the proof, we introduce a suitable generalization of the original van der Put series. We use the concept of approximability of continuous functions to give numerical examples.