Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal Approximately Convex Functions and Estimating the Size of
  Convex Hulls   A real valued function $f$ defined on a convex $K$ is anemconvex function iff
it satisfies $$ f((x+y)/2) \le (f(x)+f(y))/2 + 1. $$ A thorough study of
approximately convex functions is made. The principal results are a sharp
universal upper bound for lower semi-continuous approximately convex functions
that vanish on the vertices of a simplex and an explicit description of the
unique largest bounded approximately convex function~$E$ vanishing on the
vertices of a simplex.
  A set $A$ in a normed space is an approximately convex set iff for all
$a,b\in A$ the distance of the midpoint $(a+b)/2$ to $A$ is $\le 1$. The bounds
on approximately convex functions are used to show that in $\R^n$ with the
Euclidean norm, for any approximately convex set $A$, any point $z$ of the
convex hull of $A$ is at a distance of at most
$[\log_2(n-1)]+1+(n-1)/2^{[\log_2(n-1)]}$ from $A$. Examples are given to show
this is the sharp bound. Bounds for general norms on $R^n$ are also given.

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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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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: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph