Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Support-type properties of convex functions of higher order and
  Hadamard-type inequalities   It is well-known that every convex function admits an affine support at every
interior point of a domain. Convex functions of higher order (precisely of an
odd order) have a similar property: they are supported by the polynomials of
degree no greater than the order of convexity. In this paper the attaching
method is developed. It is applied to obtain the general result Theorem 2, from
which the mentioned above support theorem and some related properties of convex
functions of higher (both odd and even) order are derived. They are applied to
obtain some known and new Hadamard-type inequalities between the quadrature
operators and the integral approximated by them. It is also shown that the
error bounds of quadrature rules follow by inequalities of this kind.

13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph