Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sufficient conditions for univalence and study of a class of meromorphic
  univalent functions   In this article we consider the class $\mathcal{A}(p)$ which consists of
functions that are meromorphic in the unit disc $\ID$ having a simple pole at
$z=p\in (0,1)$ with the normalization $f(0)=0=f'(0)-1 $. First we prove some
sufficient conditions for univalence of such functions in $\ID$. One of these
conditions enable us to consider the class $\mathcal{V}_{p}(\lambda)$ that
consists of functions satisfying certain differential inequality which forces
univalence of such functions. Next we establish that
$\mathcal{U}_{p}(\lambda)\subsetneq \mathcal{V}_{p}(\lambda)$, where
$\mathcal{U}_{p}(\lambda)$ was introduced and studied in \cite{BF-1}. Finally,
we discuss some coefficient problems for $\mathcal{V}_{p}(\lambda)$ and end the
article with a coefficient conjecture.

1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con