Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Some Subclass of Harmonic Close-to-convex Mappings   Let $\mathcal{H}$ denote the class of harmonic functions $f$ in $\mathbb{D}:=
\{z\in \mathbb{C}:|z| < 1\}$ normalized by $f(0) = 0 = f_z(0) -1$. For $\alpha
\geq 0$, we consider the following class
$$\mathcal{W}^0_{\mathcal{H}}(\alpha):= \{f = h + \overline{g}\in\mathcal{H}:
{\rm Re\,}(h'(z) + \alpha z h''(z)) >|g'(z) + \alpha z g''(z)|, \quad z\in
\mathbb{D}\}. $$ In this paper, we first prove the coefficient conjecture of
Clunie and Sheil-Small for functions in the class
$\mathcal{W}^0_{\mathcal{H}}(\alpha)$. We also prove growth theorem,
convolution, convex combination properties for functions in the class
$\mathcal{W}^0_{\mathcal{H}}(\alpha)$. Finally, we determine the value of $r$
so that the partial sums of functions in the class
$\mathcal{W}^0_{\mathcal{H}}(\alpha)$ are close-to-convex in $|z|<r$.

27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs