  In this paper, we define a new subclass of $k$-uniformly starlike functions
of order $\gamma,\ (0\leq\gamma<1)$ by using certain generalized $q$-integral
operator. We explore geometric interpretation of the functions in this class by
connecting it with conic domains. We also investigate $q$-sufficient
coefficient condition, $q$-Fekete-Szeg\"{o} inequalities, $q$-Bieberbach-De
Branges type coefficient estimates and radius problem for functions in this
class. We conclude this paper by introducing an analogous subclass of
$k$-uniformly convex functions of order $\gamma$ by using the generalized
$q$-integral operator. We omit the results for this new class because they can
be directly translated from the corresponding results of our main class.
