Sakaguchi type functions defined by q-Bernoulli numbers

Abstract

This study uses a q-derivative operator and q-Bernoulli numbers to establish the subclass \({\mathcal {S}}\mathfrak {B}_{q,\lambda }^{s,b}\left( \mathcal {F}_{0}\right) \) of Sakaguchi type functions. We obtained constraints for the initial coefficients \(\vert a_2 \vert \) and \(\vert a_3 \vert \) through our analysis, providing insight into the characteristics and behavior of functions in this subclass. Furthermore, we derive the Fekete-Szegö inequality that is peculiar to this class, along with a number of corollaries that expand on our results and enhance our comprehension of their implications.