Estimate of Third and Fourth Hankel Determinants for Certain Subclasses of Analytic Functions.

In geometric function theory, the estimation of upper bound of the Hankel determinants for various subclasses of analytic functions is an interesting topic of current research. Till now, extensive work has been done on the estimation of second and third Hankel determinants. The present investigation deals with the estimate of fourth Hankel determinant for certain subclasses of analytic functions in the open unit disc E = {z: |z| < 1}. This work will set the stage in the direction of investigation of fourth Hankel determinant for several other classes. [ABSTRACT FROM AUTHOR]