  The theory of $q$-analogs frequently occurs in a number of areas, including
the fractals and dynamical systems. The $q$-derivatives and $q$-integrals play
a prominent role in the study of $q$-deformed quantum mechanical simple
harmonic oscillator. In this paper, we define a symmetric $q$-derivative
operator and study new family of univalent functions defined by use of that
operator. We establish some new relations between functions satisfying analytic
conditions related to conical sections.
