On Hankel determinant problems of functions associated to the lemniscate of Bernoulli and involving conjugate points

The notion of Hankel determinant Hq in univalent functions theory is initiated by Noonan and Thomas while studying it for areally mean multivalent mappings. This determinant has significant role while dealing with singularities and particularly it’s important for analyzing integral coefficient. Fekete-Szeg¨o functional used in the study of the area theorem is a particular case of this determinant. We explore a known class of holomorphic mappings which is related with the various classes of functions with conjugate symmetric points We also study upper bounds in different settings of the coefficients of these mappings. We also relate our exploration with the existing literature of the subject.