Sharp coefficient bounds for a class of symmetric starlike functions involving the balloon shape domain.

Recent research has extensively explored classes of starlike and convex functions across various domains. This study introduces a novel class of symmetric starlike functions with respect to symmetric points and associated with the balloon shape domain. We establish the explicit representation of all functions in this class. We determine the sharp bounds for the initial four coefficients, the sharp Fekete-Szegö inequality, and the sharp bound for the second Hankel determinant for every function in the newly defined class. Furthermore, we present the new findings on the inverse and logarithmic coefficients sharp bounds for all functions belonging to this class.