Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kantorovich's theorem on Newton's method for solving strongly regular
  generalized equation   In this paper we consider the Newton's method for solving the generalized
equation of the form $ f(x) +F(x) \ni 0, $ where $f:{\Omega}\to Y$ is a
continuously differentiable mapping, $X$ and $Y$ are Banach spaces,
$\Omega\subseteq X$ an open set and $F:X \rightrightarrows Y$ be a set-valued
mapping with nonempty closed graph. We show that, under strong regularity of
the generalized equation, concept introduced by S.M.Robinson in [27], and
starting point satisfying the Kantorovich's assumptions, the Newton's method is
quadratically convergent to a solution, which is unique in a suitable
neighborhood of the starting point. The analysis presented based on Banach
Perturbation Lemma for generalized equation and the majorant technique, allow
to unify some results pertaining the Newton's method theory.

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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg