Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of mixed n-Jordan homomorphisms and pseudo n-Jordan
  homomorphisms   In this article, a new notion of $n$-Jordan homomorphism namely the mixed
$n$-Jordan homomorphism is introduced. It is proved that how a mixed
$(n+1)$-Jordan homomorphism can be a mixed $n$-Jordan homomorphism and vice
versa. By means of some examples, it is shown that the mixed $n$-Jordan
homomorphisma are different from the $n$-Jordan homomorphisms and the pseudo
$n$-Jordan homomorphisms. As a consequence, it shown that every mixed Jordan
homomorphism from Banach algebra $\mathcal{A}$ into commutative semisimple
Banach algebra $\mathcal{B}$ is automatically continuous. Under some mild
conditions, every unital pseudo $3$-Jordan homomorphism can be a homomorphism.

27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs