On a Class of Multivalent Functions with Negative Coefficients Involving (r, q)− Calculus

Abstract

In this research, we focused on presenting a novel subclass of multivalent analytic functions situated in the open unit disk, characterized by the use of Jackson’s derivative operator. Our investigation systematically establishes the requisite inclusion conditions in this class, offering detailed coefficient characterizations. The exploration encompasses an array of significant properties intrinsic to this subclass, encompassing coefficient estimates, growth and distortion theorems, identification of extreme points, and the determination of the radius of starlikeness and convexity for functions falling within this specialized category. Expanding the preliminary findings, this research extended the inquiry to delve deeper into the intriguing features and implications associated with this new subclass of multivalent analytic functions. The research concentrated the light on the nuanced intricacies of coefficient estimates, providing a comprehensive understanding of how these functions evolve within the open unit disk through exploring the growth and distortion theorems, unraveling the underlying mathematical principles governing the behavior of functions in this subclass as they extend beyond the unit disk. The findings of this research contribute to the broader understanding of multivalent analytic functions, paving the way for further exploration and applications in diverse mathematical contexts.