Subclass of k-uniformly starlike functions defined by the 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 quantummechanical simple harmonic oscillators. We define a symmetric operator of q -derivative and study a new family of univalent functions defined by using this operator. We establish some new relations between the functions satisfying the analytic conditions related to conic sections.