Utilizing the q-shaba differential operator on a specific category of analytic functions

Abstract

The current investigation introduces a fresh category of analytic functions by utilizing the differential operator referred to as the q-Shaba operator. Termed as the q-Shaba differential operator throughout this study, it plays a crucial role in defining this innovative subset of functions. Moreover, the research expands and builds upon prior findings by employing the q-Shaba differential operator on various previously defined subsets and their associated outcomes. The primary objectives of this research include computing the coefficients, along with the second and third Hankel determinants and Fekete-Szego estimates, for the recently established group of functions. Additionally, the study seeks to examine the upper limits of the coefficients |dk| required for the functions f(ξ) to fall within this newly introduced classification. © 2024 IEEE.