The aim of this paper is to establish the coefficient estimates for the subclasses ofq-starlike andq-convex functions with respect to symmetric points involvingq-difference operator. Also certain applications based on these results for subclasses of univalent functions defined by convolution are given.

Quasi-subordination is an underlying concept in the area of complex function theory. It is an interesting topic that unifies the concept of both subordination and majorization. There has been no work in this area for the past three decades except possibly a recent article (Haji Mohd and Darus, Fekete-Szegö problems for quasi-subordination classes, Abstr. Appl. Anal. 2012Anal. (2012 192956, 14 p.) [8]. Exploiting this article, we provide an estimate with k-th root transform for certain classes of analytic univalent functions using quasisubordination. The authors sincerely hope that this article will revive this concept and encourage other researchers to work in this quasi-subordination in the near-future in the area of complex function theory.

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