On certain subclasses of analytic functions involving Carlson-Shaffer operator and related to lemniscate of Bernoulli (Q2338819)

Summary: The object of the present investigation is to solve the Fekete-Szegő problem and determine the sharp upper bound to the second Hankel determinant for a new class \(\mathcal R(a,c)\) of analytic functions involving the Carlson-Shaffer operator in the unit disk. We also obtain a sufficient condition for normalized analytic functions in the unit disk to be in this class.