Bounds of Third Hankel Determinant for the Family of Analytic Functions Defined With Subordination

This paper is concerned with the estimation of upper bound of the third order Hankel determinant for a unified subclass of analytic functions in the open unit disc E={z∈C:|z|<1}. Also the sharp upper bounds for the first four coefficients, Fekete-Szegö inequality, Zalcman inequality and second Hankel determinant, are established. The results are further extended for two-fold and three-fold symmetric functions.