Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed points theorems for unsaturated and saturated classes of
  contractive mappings in Banach spaces   Based on the technique of enriching contractive type mappings, a technique
that has been used successfully in some recent papers, we introduce the concept
of {\it saturated} class of contractive mappings. We show that, from this
perspective, the contractive type mappings in the metric fixed point theory can
be separated into two distinct classes, unsaturated and saturated, and that,
for any unsaturated class of mappings, the technique of enriching contractive
type mappings provides genuine new fixed point results. We illustrate the
concept by surveying some significant fixed point results obtained recently for
five remarkable unsaturated classes of contractive mappings. In the second part
of the paper, we also identify some classes of saturated classes of contractive
mappings, whose main feature is that they cannot be enlarged by means of the
technique of enriching the contractive mappings.

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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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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: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga