Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The magnitude of the minimal displacement vector for compositions and
  convex combinations of firmly nonexpansive mappings   Maximally monotone operators and firmly nonexpansive mappings play key roles
in modern optimization and nonlinear analysis. Five years ago, it was shown
that if finitely many firmly nonexpansive operators are all asymptotically
regular (i.e., the have or "almost have" fixed points), then the same is true
for compositions and convex combinations. In this paper, we derive bounds on
the magnitude of the minimal displacement vectors of compositions and of convex
combinations in terms of the displacement vectors of the underlying operators.
Our results completely generalize earlier works. Moreover, we present various
examples illustrating that our bounds are sharp.

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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph