WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
On a Class of Multivalent Functions with Negative Coefficients Involving (r, q)− Calculus
Authors: , ,
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.
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Keywords: Analytic function, Unit disk, New subclass, p−valent function, Quantum or (r, q)-Calculus, (r, q)-Derivative operator
Pages: 253-261
DOI: 10.37394/23206.2024.23.27