A Study of New Class of Star-Like Functions Associated by Symmetric p , q -Calculus

Abstract

As of late quantum calculus is broadly utilized in different parts of mathematics. Uniquely, the hypothesis of univalent functions can be newly portrayed by utilizing $q$ -calculus. In this paper, we utilize our recently presented symmetric $\left(p,q\right)$ -number ${\left[\tilde{m}\right]}_{{}_{\left(p,q\right)}}$ to characterize new symmetric $\left(p,q\right)$ -derivative ${\mathfrak{D}}_{\left(p,q\right)}$ of analytic function $f$ in the open unit disk $\mathbb{U}$ . Utilizing ${\mathfrak{D}}_{\left(p,q\right)}$ , we introduce new class of analytic star-like functions and examine some fascinating results.