A NEW q-FRACTIONAL INTEGRAL OPERATOR AND ITS APPLICATIONS TO THE COEFFICIENT PROBLEM INVOLVING THE SECOND HANKEL DETERMINANT FOR q-STARLIKE AND q-CONVEX FUNCTIONS.

In this article, we introduce and study a new q-fractional integral operator which essentially stems from a successive application of the Srivastava-Owa operator of fractional integration with the q-Ruscheweyh derivative operator. As an application of this new q-fractional integral operator, we investigate a coefficient problem involving the second Hankel determinant H²₂(f) for normalized analytic and univalent functions f(z) belonging to some normalized families of q-starlike and q-convex functions in the open unit disk U. [ABSTRACT FROM AUTHOR]