  Let $ \mathcal{S}(p) $ be the class of all meromorphic univalent functions
defined in the unit disc $ \mathbb{D} $ of the complex plane with a simple pole
at $ z=p $ and normalized by the conditions $ f(0)=0 $ and $ f^{\prime}(0)=1 $.
In this paper, we find radius of concavity and compute the same for functions
in $ \mathcal{S}(p) $ and for some other well-known classes of functions on
unit disk. We explore general linear combinations
$F(z):=\lambda_1f_1(z)+\cdots+\lambda_{2n} f_{2n}(z),\; \lambda_j\in\mathbb{C}
$, $ n\in\mathbb{N} $, of functions belonging to the class $\mathcal{S}(p)$ and
some other classes of functions of analytic univalent functions and investigate
their radii of univalence, convexity and concavity.
