Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Majorization fixed point principle and application to nonlinear integral
  equations   The successive approximations method allows us to solve problems concerning
existence and uniqueness of fixed points of wide classes of operators. The
classical result in this field, such as Banach -- Caccioppoli principle
together with some its modification and generalisations, is applicable to
operators satisfying Lipschitz condition with a small coefficient or, in other
words, to operators with the compression property. However, the successive
approximations method works well for other classes of operators that are not
compressions. In particular, the well known Kantorovich fixed point principle
for differentiable operators deals with operators that, in general, are not
compression; moreover, this principle covers some cases when Banach --
Caccioppoli principle is nonapplicable. In the article it is presented some
modification of Kantorovich fixed point principle that covers nondifferentiable
operators. We describe the exact (unimprovable) estimates of the internal and
external radius of the domain of existence of a unique fixed point of the
operator under consideration and, in addition, we present new apriori and
aposteriori error estimates for successive approximations to the corresponding
fixed point. Some applications of the new fixed point principle to nonlinear
integral operators of different types are given as well.

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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: comp-gas