Some coefficient properties of a certain family of regular functions associated with lemniscate of Bernoulli and Opoola differential operator

In this exploration, we introduce a certain family of regular (or analytic) functions in association with the righthalf of the Lemniscate of Bernoulli and the well-known Opoola differential operator. For the regular function \(f\) studied in this work, some estimates for the early coefficients, Fekete-Szegö functionals and second and third Hankel determinants are established. Another established result is the sharp upper estimate of the third Hankel determinant for the inverse function \(f⁻¹\) of \(f\).