HANKEL DETERMINANT FOR CERTAIN SUBCLASS OFUNIVALENT FUNCTIONS DEFINED BY q-DIFFERENCEOPERATOR

Abstract

 The most powerful tool that cannot be completely eroded in the
history of Geometric Functions Theory (GFT) is determinant of any order.
There is no gaining-saying that determinants have series of applications in Sciences, Engineering, Data analysis, Computing, and generally in other sectors of man’s endeavor. In particular, the Hankel determinant has attracted attention of numerous researchers possibly because of its distinct geometric structural sequence, and despite gaining so much attention there still exist some perceived gaps in knowledge that are yet to be explored. It is on this positive direction that this present study derived its interest so that a new development in knowledge can be reached. The method used the q- Difference Operator with the
second Hankel determinant as well as its inverse functions of order two along with the concept of subordination principle. With this approach in focus,this study examined some new subclasses of analytic functions. The sharp initial coefficient bounds obtained were used to derive some new subclasses of the Second Hankel along with its inverse functions.