Subclass of $k$-uniformly starlike functions defined by symmetric $q$-derivative operator

Abstract

The theory of $q$-analogs is frequently encountered in numerous areas, including fractals and dynamical systems. The $q$-derivatives and $q$-integrals play an important role in the study of $q$-deformed quantum-mechanical simple harmonic oscillators. We define a symmetric $q$-derivative operator and study a new family of univalent functions defined by using this operator. We establish some new relations between the functions satisfying analytic conditions related to conical sections.