New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-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.

Keywords

• analytic functions
• univalent functions
• quantum-calculus
• <i>q</i>-convex and <i>q</i>-starlike functions
• subordination
• Sălăgean <i>q</i>-differential operator shell-like curve