Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Kantorovich's theorem for Newton's method for solving generalized
  equations under the majorant condition   In this paper we consider a version of the Kantorovich's theorem for solving
the generalized equation $F(x)+T(x)\ni 0$, where $F$ is a Fr\'echet derivative
function and $T$ is a set-valued and maximal monotone acting between Hilbert
spaces. We show that this method is quadratically convergent to a solution of
$F(x)+T(x)\ni 0$. We have used the idea of majorant function, which relaxes the
Lipschitz continuity of the derivative $F'$. It allows us to obtain the optimal
convergence radius, uniqueness of solution and also to solving generalized
equations under Smale's condition.

1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ