Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some new Karamata type inequalities and their applications to some
  entropies   Some new inequalities of Karamata type are established with a convex function
in this paper. The methods of our proof allow us to obtain an extended version
of the reverse of Jensen inequality given by Pe{\v} cari\'c and Mi\'ci\'c.
  Applying the obtained results, we give reverses for information inequality
(Shannon inequality) in different types, namely ratio type and difference type,
under some conditions. Also, we provide interesting inequalities for von
Neumann entropy and quantum Tsallis entropy which is a parametric extension of
von Neumann entropy. The inequality for von Neumann entropy recovers the
non-negativity and gives a refinement for the weaker version of Fannes's
inequality for only special cases. Finally, we estimate bounds for the Tsallis
relative operator entropy.

31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg