Connecting Quantum Calculus and Harmonic Starlike Functions

Abstract

Quantum calculus or $q-$ calculus plays an important role in hypergeometric series, quantum physics, operator theory, approximation theory, sobolev spaces, geometric functions theory and others. But role of  $q-$ calculus in the theory of harmonic univalent functions is quite new. In this paper, we make an attempt to connect quantum  calculus and harmonic univalent starlike functions. In particular, we introduce and investigate the properties of $q-$ harmonic functions and $q-$ harmonic starlike functions of order $\alpha$.