Exploring a distinct group of analytical functions linked with Bernoulli’s Lemniscate using the 𝑞-derivative

Abstract

This research presents a new group of mathematical functions connected to Bernoulli’s Lemniscate, using the 𝑞-derivative. Expanding on previous studies, the research concentrates on determining coefficient approximations, the Fekete-Szego functional, Zalcman inequality, Krushkal inequality, along with the second and third Hankel determinants for this recently established collection of functions. Additionally, the study derives the Fekete-Szego inequality for the function 𝜉 𝑓(𝜉) and obtains the inverse function 𝑓−1(𝜉) for this specific class. This research advances our understanding in this area and suggests for further exploration