New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of q-Starlike and q-Convex Functions Associated with the Cardioid Domain

Abstract

In this paper, we define a new family of q-starlike and q-convex functions related to the cardioid domain utilizing the ideas of subordination and the Sălăgean quantum differential operator. The primary contribution of this article is the derivation of a sharp inequality for the newly established subclasses of q-starlike and q-convex functions in the open unit disc U. For this novel family, bounds of the first two Taylor–Maclaurin coefficients, the Fekete–Szegö-type functional, and coefficient inequalities are studied. Furthermore, we also investigate some new results for the inverse function belonging to the classes of q-starlike and q-convex functions. The results presented in this article are sharp. To draw connections between the early and present findings, several well-known corollaries are also highlighted. Symmetric quantum calculus operator theory can be used to investigate the symmetry properties of this new family of functions.