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Exploring a distinct group of analytical functions linked with Bernoulli's Lemniscate using the q-derivative
Isra Al-Shbeil1, Timilehin Gideon Shaba2, Alina Alb Lupas3
1Department of Mathematics, University of Jordan, Amman 11942, Jordan.
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 and obtains the inverse function for this specific class. This research advances our understanding in this area and suggests for further exploration.
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