Certain New Applications of Symmetric <i>q</i>-Calculus for New Subclasses of Multivalent Functions Associated with the Cardioid Domain

Abstract

In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We examine a wide range of interesting properties for functions that can be classified into these newly defined classes, such as estimates for the bounds for the first two coefficients, Fekete–Szego-type functional and coefficient inequalities. All the results found in this research are sharp. A number of well-known corollaries are additionally taken into consideration to show how the findings of this research relate to those of earlier studies.

Keywords

• analytic functions
• symmetric quantum calculus
• multivalent functions
• symmetric q-difference operator
• cardioid domain
• multivalent q-starlike and q-convex functions