Third Hankel Determinant for a Subfamily of Holomorphic Functions Related with Lemniscate of Bernoulli

Abstract

The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szegö functional and the third Hankel determinant for a certain subclass SL∗u,v,α of holomorphic functions defined by the Carlson-Shaffer operator in the unit disk. Finally, for some special values of parameters, several corollaries were presented.

Keywords

• Hankel determinant
• Carlson–Shaffer operator
• Lemniscate of Bernoulli
• holomorphic function
• univalent function
• Fekete-Szegö problem