Abstract
An important result of Ito and Izumi about a Diophantine inequality and the linearity of the Artin approximation function has been generalized recently by Hickel, Ito and Izumi for any excellent Henselian local domain. Our objective is to show that their results are also true in the case when R is an analytically irreducible Henselian local domain (without the excellence hypothesis). (C) 2014 Elsevier B.V. All rights reserved.