Third Hankel Determinant for a Subclass of Univalent Functions Associated with Lemniscate of Bernoulli

Abstract

This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We find the upper bound of the Hankel determinant H3(1) for this subclass by applying the Carlson–Shaffer operator to it. The present work also deals with certain properties of this newly defined subclass, such as the upper bound of the Hankel determinant of order 3, coefficient estimates, etc.

Keywords

• Hankel determinant
• Carlson–Shaffer operator
• analytic functions
• lemniscate of Bernoulli
• starlike functions