Andrei Khrennikov and Ekaterina Yurova AxelssonGeneralization of Hensel's lemma: finding the roots of $p$adic Lipschitz functions.Abstract
We consider the problem of finding the roots of $p$adic functions. In
the case, where the function is defined by a polynomial with
integer $p$adic coefficients, using Hensel's lifting lemma helps us find
the roots of the $p$adic function.
We generalize Hensel's lifting lemma for a wider class of $p$adic
functions, namely, the functions which satisfy the Lipschitz condition
with constant $p^{k}$, $k>=0$, in particular, the functions of this class
may be nondifferentiable. The paper also presents an iterative
procedure
for finding approximate (in $p$adic metric) values of the root of
$p^{k}$Lipschitz functions, thus generalizing the $p$adic analogue of
Newton's method for such a class of functions.
